Finding the area between ${y=x^2}$ and ${y=2x+8}$

Question

The two equations are ${y=x^2}$ and ${y=2x+8}$ I got the result ${-64}$ multiple times, but the proper answer seems to be different

Answer 1

The answer is supposed to be an area; therefore, it cannot be negative.

The intersection points of those two curves are $(-2,4)$ and $(4,16)$. When $x\in(-2,4)$, $x^2<2x+8$. So, the area is$$\int_{-2}^42x+8-x^2\,\mathrm dx=36.$$