Answer
$\int_{a}^{b}cf(x)~dx = c\int_{a}^{b}f(x)~dx$
Work Step by Step
We can use the definition of the integral in theorem 4 to prove Property 3:
$\int_{a}^{b}cf(x)~dx = \lim\limits_{n \to \infty}\sum_{i=1}^{n}cf(x_i)\Delta x$
$\int_{a}^{b}cf(x)~dx = c\times (\lim\limits_{n \to \infty}~\sum_{i=1}^{n}f(x_i)\Delta x)$
$\int_{a}^{b}cf(x)~dx = c\int_{a}^{b}f(x)~dx$
