Explanation

(a)
Equation of curve are $y = 0$ …(i)
and $y = 4 + 3x - x^{2}$ …(ii)
On solving Eqs. (i) and (ii), we get
$x = - 1,\ 4$
$\therefore$ Curve does not intersect $x$-axis between $x = - 1$ and $x = 4$
$\therefore$ Required area $= \int_{- 1}^{4}{\left( 4 + 3x - x^{2} \right)dx}$
$= \left\lbrack 4x + \frac{3x^{2}}{2} - \frac{x^{3}}{3} \right\rbrack_{- 1}^{4}$
$= \left\lbrack 16 + 24 - \frac{64}{3} + 4 - \frac{3}{2} - \frac{1}{3} \right\rbrack$
$= 44 - \frac{65}{3} - \frac{3}{2}$
$= \frac{264 - 130 - 9}{6} = \frac{125}{6}$ sq unit