Answer:
407/3
Step-by-step explanation:
See picture attached
Factorizing the polynomial we get
[tex]\bf y=x^2+x-6\Rightarrow y=(x+3)(x-2)[/tex]
and we can see the area is below the x-axis when -3<x<2
Hence, the are we are trying to compute is
[tex]\bf \displaystyle\int_{-5}^{-3}(x^2+x-6)dx-\displaystyle\int_{-3}^{2}(x^2+x-6)dx+\displaystyle\int_{2}^{7}(x^2+x-6)dx=\\\\=\displaystyle\int_{-5}^{-3}x^2dx+\displaystyle\int_{-5}^{-3}xdx-\displaystyle\int_{-5}^{-3}6dx\\\\-\displaystyle\int_{-3}^{2}x^2dx-\displaystyle\int_{-3}^{2}xdx+\displaystyle\int_{-5}^{-3}6dx\\\\+\displaystyle\int_{2}^{7}x^2dx+\displaystyle\int_{2}^{7}xdx-\displaystyle\int_{2}^{7}6dx[/tex]
= 98/3+8-12-35/3-(-5/2)+12+335/3+45/2-30 = 407/3
