Primitive function/Definite integral/Notation

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

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

a primitive function for a function ${}f\colon I\rightarrow \mathbb {R}$. Suppose that ${}a,b\in I$. Then one sets

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