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 $\closedint a b$.

Let $F$ be a real function which is defined on $\closedint a b$ by:
 * $\displaystyle \map F x = \int_a^x \map f t \rd t$

Then:
 * $\displaystyle \frac \d {\d x} \int_a^x \map f t \rd t = \map f x$

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