Definite Integral of Constant Multiple of Real Function

Theorem
Let $f$ be a real function which is integrable on the closed interval $\left[{a \,.\,.\, b}\right]$.

Let $c \in \R$ be a real number.

Then:


 * $\displaystyle \int_a^b c f \left({x}\right) \rd x = c \int_a^b f \left({x}\right) \rd x$