plot and fill region

\documentclass{article}
\usepackage{pgfplots}
\usepgfplotslibrary{fillbetween}
\begin{document}
\begin{figure}[!h]
\centering
\begin{tikzpicture}
\begin{axis}[
  axis x line=center,
  axis y line=center,
  xmin=-0.1,
  xmax=1.1,
  ymin=-0.1,
  ymax=1.1,
  xtick={1},
  ytick={1},
  xlabel=$x$,
  ylabel=$y$,
  x label style={anchor=west},
  y label style={anchor=south}]
\node[below] at (axis cs:0.02,0){$0$};
\node[right] at (axis cs:0.75,0.5){$F(x)=x^2$};
\node[left] at (axis cs:0.45,0.5){$G(x)=x$};
\addplot[domain=-0.1:1.05, name path=A]{x^2};
\addplot[domain=-0.1:1.1, name path=B]{x};
\addplot[gray!50] fill between[of=A and B, soft clip={domain=0:1}];
\end{axis}
\end{tikzpicture}
\end{figure}
\end{document}