Fundamental Theorem of Calculus/First Part

Theorem
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:
 * $\displaystyle F \left({x}\right) = \int_a^x f \left({t}\right) \rd t$

Then $F$ is a primitive of $f$ on $\left[{a \,.\,.\, b}\right]$.