Differentiation is mechanics, integration is art.
In many ways this statement holds true, perticularly for the case of the polynomial. You can only ever differentiate the poor things a set amount of times before all you get is zeroes. Whereas even a single integral gives you an infinite amount of possible answers to enjoy.
Now what if I told you that even for the simplest of parabola there is a sense in which differentiation can happen at an infinite level of precision, yielding more values than any of us could ever hope to comprehend. And now what if I told you that this power can be yours. Right at your fingertips, through the power of python!
Enjoy responsibly.