Definition:Absolutely Convergent Integral

Let $I = \displaystyle \int_S f\left({x}\right) \, \mathrm d x$ be an improper integral, where $S$ is an unbounded closed interval.
$I$ is absolutely convergent if and only if $\displaystyle \int_S \left \vert {f \left({x}\right)}\right\vert \, \mathrm d x$ converges.