Explanation

(a)
$Required\ area = \int_{- 1}^{2}{y\ dx = \left| \int_{- 1}^{0}{y\ dx} \right| + \int_{0}^{2}{y\ dx}}$
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$= \left| \int_{- 1}^{0}{xdx} \right| + \int_{0}^{2}{x\ dx}$
$= \left| \left\lbrack \frac{x^{2}}{2} \right\rbrack_{- 1}^{0} \right| + \left\lbrack \frac{x^{2}}{2} \right\rbrack_{0}^{2} = \frac{5}{2}\ sq\ unit$
Alternate
Required area $=$ Area of $\mathrm{\Delta}OAB +$ Area of $\mathrm{\Delta}OCD$
$\frac{1}{2} \times 2 \times 2 + \frac{1}{2} \times 1 \times 1$
$= \frac{5}{2}\ sq\ units$