Continuous Function/Primitive function exists/Fact/Proof

Proof

Let ${}a\in I$ be an arbitrary point. Due to fact, there exists the function

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

and because of the Fundamental theorem, the identity ${}F'(x)=f(x)$ holds. This means that ${}F$ is a primitive function for ${}f$.

To fact