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

The region is bounded by $y = x + 2$, $x = 0$, $x = 1$, and $y = 0$.

Key points on the line $y = x + 2$:

When $x = 0$:

$y = 0 + 2 = 2$

Point: $(0, 2)$

When $x = 1$:

$y = 1 + 2 = 3$

Point: $(1, 3)$

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The bounded region forms a trapezoid with:

Bottom side: along the x-axis from $(0,0)$ to $(1,0)$

Left side: vertical line from $(0,0)$ to $(0,2)$ with height $= 2$

Right side: vertical line from $(1,0)$ to $(1,3)$ with height $= 3$

Top side: line $y = x + 2$

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Using the trapezoid area formula:

Area $= \dfrac{1}{2} \times (\text{sum of parallel sides}) \times \text{width}$

Sum of parallel sides $= 2 + 3 = 5$

Width $= 1 - 0 = 1$

Area $= \dfrac{1}{2} \times 5 \times 1$

Area $= \dfrac{5}{2}$ sq. units