Antiderivative on an Interval

Let $I$ be an interval in the sense of Interval in the Real Line. A function $F:I\to\mathbb{R}$ is an antiderivative of a function $f:I\to\mathbb{R}$ on $I$ if $F$ is differentiable at every interior point of $I$ in the sense of Derivative at an Interior Point and satisfies $F'(x)=f(x)$ for every interior point $x\in I$.