You are given the four points in the plane $A = (-5,2)$, $B = (0,-8)$, $C = (4,2)$, and $D = (8,-4)$. The graph of the function $f(x)$ consists of the three line segments $AB$, $BC$ and $CD$. Find the integral $\displaystyle \int_{-5}^{8} f(x)\,dx$ by interpreting the integral in terms of sums and/or differences of areas of elementary figures.

$\displaystyle \int_{-5}^{8} f(x)\,dx =$