Primitive of Pointwise Sum of Functions

Theorem
Let $f_1, f_2, \ldots, f_n$ be real functions which are integrable.

Then:


 * $\ds \int \map {\paren {f_1 \pm f_2 \pm \, \cdots \pm f_n} } x \rd x = \int \map {f_1} x \rd x \pm \int \map {f_2} x \rd x \pm \, \cdots \pm \int \map {f_n} x \rd x$