from a practical perspective, you can mostly think of integration and differentiation as inverse operations. (it works fine for most functions that come up in most applications.)

but this doesnt really hold true in general. a famous example is that the gaussian distribution (used to make bell curves) is an integral that cannot be solved by using differentiation to "undo" integration. the general problem is that its a lot easier for a function to be integrable than it is for a function to be differentiable. (all continuous functions are integrable, but not all continuous functions are differentiable. even more troubling, there are integrable functions that aren't even continuous.)