Fundamental Theorem of Calculus/Second Part

Theorem
Let $f$ be a real function which is continuous on the closed interval $\left[{a \,.\,.\, b}\right]$.

Then:
 * $f$ has a primitive on $\left[{a \,.\,.\, b}\right]$
 * If $F$ is any primitive of $f$ on $\left[{a \,.\,.\, b}\right]$, then:
 * $\displaystyle \int_a^b f \left({t}\right) \ \mathrm d t = F \left({b}\right) - F \left({a}\right) = \left[{ F \left({t}\right) }\right]_a^b$