The fundamental theorem of calculus comes in two parts.
One part relates definite integrals to anti-derivatives:

(Second) Fundamental Theorem of Calculus:

If $F'(x)=f(x)$, then $$\int_a^b f(x)\, dx = F(b) - F(a).$$

In other words, the (definite) integral of the derivative (of $F(x)$)
is the change in the original function. This also gives us an incredibly
powerful way to compute definite integrals:

Find an anti-derivative.

Evaluate at the endpoints.

In practice, 99% of all integrals are computed this way.

Or as Shakespeare put it: Tomorrow, and tomorrow, and tomorrow,
Creeps in this petty pace from day to day,
To the last syllable of recorded time
(Macbeth Act 5, Scene 5)