The area (in sq. units) of the region bounded by the line $y = x+2, x = 0, x = 1$ and $y = 0$ is

$\frac{5}{2}$

The correct answer is Option (2) → $\frac{5}{2}$

Given region is bounded by

$y=x+2,\;y=0,\;x=0,\;x=1$

Required area

$\int_{0}^{1}(x+2-0)\,dx$

$=\int_{0}^{1}(x+2)\,dx$

$=\left[\frac{x^2}{2}+2x\right]_{0}^{1}$

$=\frac{1}{2}+2$

$=\frac{5}{2}$

The required area is $\frac{5}{2}$ square units.