Main theorem of calculus/Riemann/Newton-Leibniz-formula/Fact

Newton-Leibniz-formula

Let ${}I$ denote a real interval, and let

$f\colon I\longrightarrow \mathbb {R}$

denote a continuous function. Suppose that ${}F$ is a primitive function for ${}f$.

Then for

${}a,b\in I$, the identity

${}\int _{a}^{b}f(t)\,dt=F(b)-F(a)\,$

holds.

Proof, Write another proof