Maybe something like: When you do derivation you analyze how the function behaves at a given point. Whenever you analyze something you analyze a given thing, not all things. When you do integration you look at a function and then produce something that describes the function on every point. You come up with a closed integral-formula for the shole function. You need to synthesize something that describes the function everywhere. But when you derivate the dericate, you also produce a closed function that describes the function everywhere. Oops, I think I got lost here too.