Riemann integrable function/Integral function/Definition

Integral function

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

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

denote a Riemann-integrable function, and let ${}a\in I$. Then the function

$I\longrightarrow \mathbb {R} ,x\longmapsto \int _{a}^{x}f(t)\,dt,$

is called the integral function for ${}f$ for the starting point ${}a$.