You are given the three points in the plane $A = (-5,-4)$, $B = (-3,7)$, and $C = (2,0)$. The graph of the function $f(x)$ consists of the two line segments $AB$ and $BC$ . Find the integral $\displaystyle \int_{-5}^{2} f(x)\,dx$ by interpreting the integral in terms of sums and/or differences of areas of elementary figures.
$\displaystyle \int_{-5}^{2} f(x)\,dx =$