y $$-$$ x = 2, x² = y

Now, x² = 2 + x

$$\Rightarrow$$ x² $$-$$ x $$-$$ 2 = 0

$$\Rightarrow$$ (x + 1)(x $$-$$ 2) = 0

Area = $$\int\limits_{ - 1}^2 {(2 + x - {x^2})} $$

$$ = \left| {2x + {{{x^2}} \over 2} - {{{x^3}} \over 3}} \right|_{ - 1}^2$$

$$ = \left( {4 + 2 - {8 \over 3}} \right) - \left( { - 2 + {1 \over 2} + {1 \over 3}} \right)$$

$$ = 6 - 3 + 2 - {1 \over 2} = {9 \over 2}$$