The area (in square units) bounded by the curve $y=|x-2|$ between $x=0, y = 0$ and $x=5$ is:

6.5

The correct answer is Option (3) → 6.5

$y=\left\{\begin{matrix}2-x,&x<2\\x-2&x≥2\end{matrix}\right.$

first triangle (from $x=0$ to $x=2$)

Area = $\frac{1}{2}×2×2=2$

Second triangle (from $x=2$ to $x=5$)

Base = 5 - 2 = 3

Height = $y(5)=|5-2|=3$

Area = $\frac{1}{2}×3×3=4.5$

∴ Total Area = $4.5+2=6.5$ sq. units