The graph of a piecewise linear function $f(x)$ is above. Evaluate $\displaystyle \int\limits_3^8 f'(x)   dx$

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Though it may be tempting to take the area under the curve, it would not lead to our answer. We need to integrate $f'(x)$ and use the graph to obtain our needed values.

$$\int \limits_3^8 f'(x)   dx = f(x)\Big]_3^8$$ $$=f(8)-f(3)$$ $$= 0 - 2$$ $$= \boxed{-2}$$