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Given the piecewise function:

$$f(x) = \begin{cases} -|x+1|+2 &x \in [-1,1)\\\ -(x-3)^2+4 &x \in [1,5] \end{cases}$$

...find the area between the curve of $f(x)$ and the x-axis on the interval $[-1, 5]$.

$2$

$\dfrac{26}{3}$

$\dfrac{32}{3}$

$\dfrac{38}{3}$