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I have posted a link there to this topic so the OP can see my work.Find the area between the curves?

Find the area between the curves y= x^2 -8, y= -2x, and x=4

The teacher says the integral setup is

Area= Integral-4 to 2) (-2x- x^2 +8)dx + Integral2 to 4) (x^2 -8 + 2x) dx

How did the teacher get that?