Official solution
Parabola : x2 = y
Straight line : y = x + 2
\[ \therefore \] x2 = x + 2
\[ \Rightarrow \] x2 - x - 2 = 0
x = -1, 2
\[ \therefore \] y = 1, 4
Required area = \[\int\limits_{ - 1}^2 {\left[ {\left( {x + 2} \right) - {x^2}} \right]} dx\]
= \[\left[ {{{{x^2}} \over 2} + 2x - {{{x^3}} \over 3}} \right]_{ - 1}^2\]
= \[\left( {2 + 4 - {8 \over 3}} \right) - \left( {{1 \over 2} - 2 + {1 \over 3}} \right)\]
= \[{{9 \over 2}}\]