Function/R/Primitive function/Definition

Primitive function

Let ${}I\subseteq \mathbb {R}$ denote an interval, and let

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

denote a function. A function

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

is called a primitive function for ${}f$, if ${}F$ is differentiable on ${}I$ and if ${}F'(x)=f(x)$ holds for all ${}x\in I$.