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:
 * $(1): \quad f$ has a primitive on $\left[{a \,.\,.\, b}\right]$
 * $(2): \quad$ If $F$ is any primitive of $f$ on $\left[{a \,.\,.\, b}\right]$, then:
 * $\displaystyle \int_a^b f \left({t}\right) \, \mathrm d t = F \left({b}\right) - F \left({a}\right) = \left[{F \left({t}\right)}\right]_a^b$