Integral of Characteristic Function

Theorem
Let $\left({X, \Sigma, \mu}\right)$ be a measure space.

Let $E \in \Sigma$ be a measurable set, and let $\chi_E: X \to \R$ be its characteristic function.

Then $I_\mu \left({\chi_E}\right) = \mu \left({E}\right)$, where $I_\mu \left({\chi_E}\right)$ is the $\mu$-integral of $\chi_E$.