Definite Integral of Constant Multiple of Real Function/Proof 2

Proof
Let $F$ be a primitive of $f$ on $\left[{a \,.\,.\, b}\right]$.

By Linear Combination of Definite Integrals


 * $\displaystyle \int_a^b \left({\lambda f \left({t}\right) + \mu g \left({t}\right)}\right) \rd t = \lambda \int_a^b f \left({t}\right) \rd t + \mu \int_a^b g \left({t}\right) \rd t$

for real functions $f$ and $g$ which are integrable on the closed interval $\left[{a \,.\,.\, b}\right]$, where $\lambda$ and $\mu$ be real numbers.

The result follows by setting $\lambda = c$ and $\mu = 0$.