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

${\displaystyle \underset{2}{\overset{\sqrt[\phantom{2}]{2}}{}}}f(x)dx=$

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