The area of the region bounded by $y=|x-5|, x=0 $ and $x=1 $ is :

$\frac{9}{2}$

The correct answer is Option (3) → $\frac{9}{2}$

$y=|x-5|$, $x=0$ to $x=1$

$y=\left\{\begin{matrix}x-5,&x≥5\\5-x,&x<5\end{matrix}\right.$

so area = $\int\limits_0^15-xdx$

$=\left[\frac{5x-x^2}{2}\right]_0^1$

$=5-\frac{1}{2}=\frac{10-1}{2}$

$=\frac{9}{2}$ sq. units