Many uses of images, quotations, and other materials in a scholarly writing would be fair use, but you cannot assume that an academic purpose automatically guarantees fair use. The key questions are basically: How are you using it? and Are you using an appropriate amount?
At one end of the spectrum, imagine a short quotation, or an image reproduced at a viewing-friendly (but not reproduction-friendly) resolution, and a article or book that discusses and critiques that image or quotation. The writer is using the material to make a particular point important to their scholarship, and adding to academic discourse on the subject. No one is going to use the new work as a substitute for the original work. Few or no copyright owners would object to this type of use as a fair use, requiring no permission, and it is hard to imagine a successful challenge if they did. The analysis generally changes little for works that will be posted on the internet; you may want to consider whether you have included, for example, so many things from the same creator at such a high quality that people would download a copy of your article rather than buying a copy of the work.
On the other end of the spectrum, imagine a writer who wants to discuss one paragraph of another writer's work, but quotes ten pages that are not discussed. Imagine a writer who includes several images from a particular artist, in a format that shows more detail than a user needs to understand the writer's text, or is suitable for poster printing. Even though the writer is creating scholarship and has a noncommercial purpose, the amount used is more than is appropriate.
Many uses will fall somewhere between these two extremes, but in our experience most scholarly uses of quotations and examples will fall closer to the first case. The nature of scholarly writing is that most external content is included because the author is making a point about it.
Often this will be fair use, but as excerpts for scholarly writing, a user cannot assume that just because a use is for a noncommercial scholarly purpose, it is automatically a fair use. Think about not only the purpose of your use, but the creator's original purpose for the use, and their primary market.
Scanning your course's textbook and adding it to Canvas to save your students some money would not be fair use, because you are not using the material in a different way or for a different purpose, and you are using so much of it. On the other hand, imagine a scenario where you're scanning sections of an old history textbook to demonstrate the racial or gender bias it exhibits, rather than for your students to learn history the way the book presents it. That would be a much different way than the book was originally written to be used, and a strong case for fair use.
For more on fair use in the context of course management systems, please see the Association for Research Libraries' pages about the Code of Best Practices in Fair Use for Academic and Research Libraries.
If you don't want to worry about whether your use is a fair one, and the work you want to use is included in a library subscription or database, you can always provide your students with a link rather than a PDF. You can do this from the UC-eLinks menu for any article. You can get to the UC-eLinks menu by entering citation information into Citation Linker.
Once you're at the UC-eLinks menu screen, look for the option to Copy & Paste Citation.
Then copy the link provided in the bottom box and add it to your Canvas site.
You could also give them a citation and have them look it up themselves in Citation Linker or other parts of the library website. They could probably use the practice!
Sometimes this is a fair use question, but often it's a question about whether the figure is even copyrightable in the first place.
Facts are not copyrightable. If particular facts can only be expressed in one way, or if they've been expressed in a very obvious and standard way that is not creative, then that expression of facts is not copyrightable. If the figure you want to use is a fairly standard graph that looks like it was made in Excel, that's probably not copyrightable and therefore permission is not required. The more creativity and design used in displaying the data, the more likely it is that a figure is copyrightable.
If you're not sure if a figure is copyrightable, or you believe that it is, you still have fair use. If you are including the figure to critique it or provide your own commentary (therefore using it for a different purpose than the original creator), and using an appropriate amount, then you have a strong argument in support of fair use and still do not need permission.
United States copyright law has Fair Use, which allows certain uses of a work without permission, regardless of what kind of notice or warning the author/copyright holder puts on something.