\documentclass{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{fourier}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usepgfplotslibrary{fillbetween}
\usetikzlibrary{patterns.meta}

\begin{document}

\begin{tikzpicture}
\begin{axis}[
  axis lines=center, 
  axis equal,
  xlabel=$x$, 
  ylabel=$y$,
  domain=-3:6,
  ymin=-4,
  ymax=4.4, 
  xmin=-3.4, 
  xmax=6.4, 
  label style={font=\scriptsize},
  tick label style={font=\scriptsize},
  xtick distance=1,
  ytick distance=1,
  fun/.style={thick, samples=80, smooth}
]

\addplot[name path=f1, fun] {-(x^3)/4+x^2+x/4+0.5};
\path[name path=ox] (0,0) -- (6,0);
\addplot[draw=black, fill=gray!50] fill between 
  [of=f1 and ox, soft clip={domain=1:3}];
\end{axis}
\end{tikzpicture}

\end{document}