If the image falls within the Public Domain or has a Creative Commons license that allows for its use with or without attribution, yes, you can use the image in the presentation/class without asking for permission from the copyright holder.
If the image is protected by copyright, using images for educational purposes is allowed under fair use exemptions to U.S. copyright (U.S. Code, Title 17, Chapter 1, Section 107.) Use of a copyrighted work for criticism, comment, news reporting, teaching, scholarship, and research are not considered infringements if the use weighs favorably when considering these four factors:
- Purpose and character of the use, including whether such use is of a commercial nature or is for nonprofit educational purposes
- Nature of the copyrighted work
- Amount and substantiality of the portion used in relation to the copyrighted work as a whole
- Effect of the use on the potential market for or value of the copyrighted work.
Generally speaking, using copyrighted images for teaching and education is considered fair use. However, if that includes posting images to a website, that could be considered a publication and therefore copyright infringement.
Fair use is not always clear and must be decided on a case-by-case basis using the four factors listed above.