Answer
$\text{The volume is}$
\begin{align}
& V =\frac{7\pi}{15}
\end{align}
Work Step by Step
$\text{It is given that}$
\begin{align}
x = y^2 \ and \ x= y
\end{align}
$\text{The function revolves around x = -1. }$
$\text{The intersections of two functions are}$
\begin{align}
y^2 = y \Rrightarrow y = 0 \ and \ y = 1 \Rrightarrow x = 0 \ and \ x = 1
\end{align}
$\text{The volume is}$
\begin{align}
& V =\pi \int_0^1 \left( (y+1)^2 - (y^2+1)^2\right)dy = \pi \int_0^1 (-y^4 -y^2+2y) dy = \\
& = \pi \left[\frac{-y^5}{5} + \frac{-y^3}{3} +y^2 \right]_0^1 =\pi \left( -\frac{1}{5} - \frac{1}{3} + 1\right) = \frac{7\pi}{15}
\end{align}
