What is differentiation? it is measuring the ratio of how the output change versus how the input changes. It is a linear map from the vector space of small change of input, to the vector space of small changes of output.

What is integration? It is a process of collecting stuff / contributions along the way.

The fundamental theorem of calculus says $$ \int_a^b f'(x) dx = f(b) - f(a).$$

There is also the chain rules, which says, if quantity x affect y,and y affect z, then x affects z. If $y=2x$, $z=3y$, then $z = 6x$.