Area bounded by y=|x-5| and x-axis between x=2; and x=4 is :

5 4 3 6

4

$y=|x-5|$, $x=2$ to $x=4$ at $x < 5$ $y=5-x$ so area = $\int\limits_2^45-xdx$ $=\left[5x-\frac{x^2}{2}\right]_2^4$ $=20-8-10+2=4$ sq. units