[commandlinefan]

> No one should go with pen an paper double checking if that polynomial integral is correct or not!

Hm - maybe I'm fortunate that I studied calculus before there were (accessible) software packages that could just do this stuff for you, because back then, the only way to solve these was to do them on paper. I'm sure I would have been tempted to just "skip ahead" to letting the computer do it for me, but I definitely learned a lot more going through all of the steps myself than I would have if I had just gotten a high-level understanding of what was going on and plugged the rest into a computer. Because, honestly, integrating polynomials is really, really easy - if you know how to do it, you can do it on paper faster than you can load up wolfram-alpha, type it in, and wait for an answer.