Is there a formal way to approach finding the area of the shaded region in this diagram? From the examples it looks like they're flipping the sign of the entire integral. Both of them, actually.

Btw, the answer is: \(\displaystyle \int_{-\sqrt{10}}^{-1}(-x^2+10)dx+\int_{-1}^{0}-9xdx\)

Btw, the answer is: \(\displaystyle \int_{-\sqrt{10}}^{-1}(-x^2+10)dx+\int_{-1}^{0}-9xdx\)

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