$(1$ point$)$ You are given the four points in the plane $A=(-1,3),B=(3,-2),C=(8,8),$ and $D=(12,-5).$ The graph of the function $f(x)$ consists of the three line segments $AB,BC$ and $CD.$ Find the integral ${\displaystyle \underset{-1}{\overset{12}{}}}f(x)dx$ by interpreting the integral in terms of sums and$/$or differences of areas of elementary figures.

${\displaystyle \underset{-1}{\overset{12}{}}}f(x)dx=$