Fundamental Theorem of Calculus/First Part/Corollary

Corollary to Fundamental Theorem of Calculus (First Part)
Let $f$ be a real function which is continuous on the closed interval $\left[{a \,.\,.\, b}\right]$.

Let $F$ be a real function which is defined on $\left[{a \,.\,.\, b}\right]$ by:
 * $\displaystyle F \left({x}\right) = \int_a^x f \left({t}\right) \ \mathrm d t$

Then:
 * $\displaystyle \frac {\mathrm d}{\mathrm dx} \int_a^x f \left({t}\right) \ \mathrm d t = f \left({x}\right)$

Proof
Follows from the Fundamental Theorem of Calculus (First Part) and the definition of primitive.