Answer
$\text{Area = 6}$
Work Step by Step
$\text{It is given that}$
\begin{align}
f(y) = y^2+1; \ g(y) = 0; \ y = -1 \ \ and \ \ y = 2
\end{align}
$\text{Thus, the area of the given region is}$
\begin{align}
Area = \int_{-1}^2 ((y^2+1) - 0) \ dy = \left[\frac{x^3}{3}+y \right]_{-1}^2 = 3 + 3 = 6
\end{align}
