The region bounded by the curves x² = y, y = x + 2 and x-axis has the area enclosed by them is:

5/6

The parabola and line meet in points P(-1,1) and Q(2, 4).

The line cuts the axes in (–2, 0) and B(0, 2).

i.e. area APR + area PRO

$=\int_{-2}^{-1}y\,dx+\int_{-1}^{0}=\int_{-2}^{-1}(x+2)dx+\int_{-1}^{0}x^2dx=[\frac{x^2}{2}+2x]_{-2}^{-1}+[\frac{1}{3}x^3]_{-1}^{0}=\frac{1}{2}+\frac{1}{3}=\frac{5}{6}$sq. units