\documentclass[tikz,border=5pt]{standalone}
\usetikzlibrary{arrows.meta, intersections, backgrounds, shapes.geometric, positioning, arrows.meta, positioning, tikzmark, patterns}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{fillbetween}
\begin{document}
\pgfmathdeclarefunction{poly}{0}{%
\pgfmathparse{-x^3+5*(x^2)-3*x-3}%
}
\begin{tikzpicture}[xscale=1.5,yscale=.5]
\begin{axis}[
xmin=-2,
xmax=5,
ymin=-5,
ymax=10,
axis y line=left,
axis x line=bottom,
xtick={-1.2,2,4.2},
xticklabels={$a$,$c$,$b$},
ytick={3},
yticklabels={$\mu=f(c)$},
samples=160
]
\addplot[name path=poly,black,thick,mark=none,domain=-1.2:4.2,stack plots=y,color=black,very thick] {poly} node[right] {$\mathcal{C}_f$};
\addplot[name path=line,gray,no markers,line width=1pt,domain=-1.2:4.2,color=red] {3};
\addplot fill between[ 
of = poly and line, 
split, % calculate segments
every even segment/.style = {pattern=north east lines, pattern color=lightgray},
every odd segment/.style  ={pattern=north east lines, pattern color=lightgray}
];
\draw[help lines] (axis cs:-1.2,-5) -- (axis cs:-1.2,3);
\draw[help lines] (axis cs:2,-5) -- (axis cs:2,3);
\draw[help lines] (axis cs:4.2,-5) -- (axis cs:4.2,3);
\draw[help lines] (-2,3) -- (-1.2,3);
\end{axis}
\end{tikzpicture}
\end{document}