Explanation

(b)
Intersection points of given curves are $( - 1,0)$ and (3,0)
$Required\ area = \int_{- 1}^{3}{\left( {- x}^{2} + 2x + 3 \right)dx}$
$= \left\lbrack \frac{x^{3}}{3} + \frac{2x^{2}}{2} + 3x \right\rbrack_{- 1}^{3}$
$= \left\lbrack - 9 + 9 + 9 - \left( \frac{1}{3} + 1 - 3 \right) \right\rbrack$
$= \frac{32}{3}\ sq\ units\$