Integration is a completely different ball game. Given an arbitrary expression, most likely it's not symbolically integrable, i.e. it's integral can't be expressed as a combination of known functions. That's why there are lots of functions defined as "the integral of blah."
Even given an expression that's known to be symbolically integrable, it's quite the puzzle to figure out what the integral is. There's no straight forward algorithm, as with differentiation. It boils down to "try integration by parts; try this; try that; maybe do some clever algebraic manipulation to get it into a form where you can try one of those things; look it up in a book of integrals to see if it's there, or something similar is there; if all else fails, guess and check."
So the paper does "guess and check," and only returns answers that pass the check, i.e. are exactly right.
There are some problems where all the checks fail, i.e. the paper can't generate an answer. And there are also questions where Matlab / Maple can't find an answer either.
* It's a little more complicated; e.g. if f = cos^2, and the derivative of F is 1 - sin^2, I need to recognize they're the same. But it's safe, in the sense that if I can't determine whether they're the same, I can reject the solution and move on to the next one.