Explanation

(a)
$Required\ area = \int_{1}^{3}{|x - 2|dx}$
$= \int_{1}^{2}{(2 - x)dx + \int_{2}^{3}{(x - 2)dx}}$
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$= \left\lbrack 2x - \frac{x^{2}}{2} \right\rbrack_{1}^{2} + \left\lbrack \frac{x^{2}}{2} - 2x \right\rbrack_{2}^{3}$
$= 2 - \frac{3}{2} - \frac{3}{2} + 2 = 1sq\ unit$
Alternate
Area$= Area\ of\ \mathrm{\Delta}AOB + Area\ of\ \mathrm{\Delta}ODC$
$= \frac{1}{2} \times 1 \times 1 + \frac{1}{2} \times 1 \times 1$
$= 1\ sq\ unit$