Primitive of Pointwise Sum of Functions/Examples/f+g

Examples of Use of Primitive of Pointwise Sum of Functions
Let $f$ and $g$ be real functions of $x$ which are integrable.

Then:
 * $\ds \int \paren {\map f x + \map g x} \rd x = \int \map f x \rd x + \int \map g x \rd x$

Proof
This is an instance of Primitive of Pointwise Sum of Functions:


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

where $f = f_1$ and $g = f_2$.