Question

How does the fundamental theorem of calculus connect derivatives and integrals?

Answer 1

The fundamental theorem of calculus shows that differentiation and integration are reverse processes of each other.

Let us look at the statements of the theorem.
(I) `d/dx int_a^x f(t)dx=f(x)`
(II) `int f'(x)dx=f(x)+C`

As you can see above, (I) shows that integration can be undone by differentiation, and (II) shows that differentiation can be undone by integration (with a loss of the information of C).