Definition:Absolutely Integrable Function

Definition
Let $f$ be a real function.

$f \left({x}\right)$ is absolutely integrable on $S \subseteq \R$ its absolute value of $f$ is an integrable function on $S$.

That is, the definite integral of the absolute value of $f$ over any interval $\left[{\alpha \,.\,.\, \beta}\right] \subseteq S$ is bounded.