Mathematics

Problem

Which of the following definite integrals represents the area of the region that is bounded on the left by the curve

x = y^{2}

, on the right by the line

x = y + 2

, and between the horizontal lines

y=-1

and

y=2

? a)

\displaystyle \int_{2}^{-1}\big[(y+2)-y^{2}\big]\,dy

\displaystyle \int_{-1}^{2}\big[y^{2}-(y+2)\big]\,dy

\displaystyle \int_{-1}^{2}\big[(y+2)+y^{2}\big]\,dy

\displaystyle \int_{-1}^{2}\big[(y+2)-y^{2}\big]\,dy