The area of the region bounded by the curve $y = x + 1$ and the lines $x = 2, x = 3$, is

$\frac{7}{2}$ sq units

The correct answer is Option (1) → $\frac{7}{2}$ sq units

Required area of the shaded region is

$A = \int_{2}^{3} (x + 1) \, dx = \left[ \frac{x^2}{2} + x \right]_{2}^{3}$

$= \left[ \frac{9}{2} + 3 - \frac{4}{2} - 2 \right] = \left[ \frac{5}{2} + 1 \right] = \frac{7}{2} \text{ sq. units}$