Fundamental Theorem of Calculus/Second Part

Theorem
Let $f$ be a real function which is continuous on the closed interval $\closedint a b$.

Then:
 * $(1): \quad f$ has a primitive on $\closedint a b$
 * $(2): \quad$ If $F$ is any primitive of $f$ on $\closedint a b$, then:
 * $\ds \int_a^b \map f t \rd t = \map F b - \map F a = \bigintlimits {\map F t} a b$