Primitive function/Definite integral/Notation

Let $I$ denote a real interval, and

$F:I⟶ℝ$

a primitive function for a function $f:I\to ℝ$. Suppose that $a,b\in I$. Then one sets

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