What is copyright infringement?
As a general matter, copyright infringement occurs when a copyrighted work is reproduced, distributed, performed, publicly displayed, or made into a derivative work without the permission of the copyright owner.
Fair Use covers what we do here. Just don't quote work without crediting the author. Link is sufficient.
I don't know anything special about cartoons other than you're quoting the work in its entirety rather than plucking quotes form an article/book. If it's a Forum rule, then that's that. Otherwise... eh...