Find the area between x=-y and x=2-y^2

Answer 1

The curves intersect at (-2,2) and (1,-1)
so, the area is the sum of all the little horizontal strips between the line and the parabola:

∫[-1,2] (2-y^2)-(-y) dy
= ∫[-1,2] 2+y-y^2 dy
= 9/2