Explanation

(d)
$Area = 4\int_{0}^{1}{(1 - x)dx = 4\left\lbrack x - \frac{x^{2}}{2} \right\rbrack_{0}^{1}}$
$= 4\left( 1 - \frac{1}{2} \right) = 2\ sq\ units$
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Alternate
From figure $ABCD$ is square, whose diagonals $AC$ and $BD$ are of length 2 unit.
$Hence,\ \ Required\ area = \frac{1}{2} \times AC \times BD$
$= \frac{1}{2} \times 2 \times 2$
$= 2\ sq\ units$