HI Hans,

Sorry, I forgot

\usemodule[pgfplots]

\pgfplotsset{compat=1.13}
\usetikzlibrary[intersections]
\usepgfplotslibrary[fillbetween]

\starttext

\starttikzpicture[/pgf/declare function={f(\x)=(1/8)*(\x^3-2.5*\x^2-3*\x+4.5);},]          
\switchtobodyfont[8pt]
\startaxis
    [restrict x to domain=-3:5, xmax=5, xmin=-3,
     restrict y to domain=-3:3, ymax=3, ymin=-3,
     x=2cm,
     y=2cm,
     axis lines=center,
     axis line style =ultra thick,
     major tick style=black,
     xtick={-2,-1,...,4},
     ytick={-2,-1,...,2},
     yticklabels={,,},
     xticklabels={,,},
     extra x ticks={-3,5},
     extra x tick label={\null},
     extra y ticks={-3,3},
     extra y tick label={\null},
     extra tick style={tick style={draw=none}},
     xlabel=$x$,ylabel=$y$,
     every axis x label/.style={
     at={(ticklabel* cs:1.01)},
     anchor=west,
},
     every axis y label/.style={
     at={(ticklabel* cs:1.01)},
     anchor=south,
},
     samples=1000,
     >=stealth]
\addplot[smooth,
         draw=none,
         tension=0.6,
         name path=plot]
coordinates{
(-2,-2.5) (-1.5,0)(-1,1.5) (-0.5,2)
(0,1.5) (1,0) (2,-0.5)
(3,0) (4,1.5)
};

\path[name path=cut line] (-2,1.5) -- (4,1.5);

\draw[thick,intersection segments={of=plot and cut line,sequence=L1}];
 
\draw[thick,intersection segments={of=plot and cut line,sequence=L2}];
  
\draw[thick, intersection segments={of=plot and cut line,sequence=L3}];

\node[fill=black,circle,scale=0.4] at (-2,-2.5){};
\node[fill=black,circle,scale=0.4] at (4,1.5){};
   
\node[below] at (-1.5,-1.5) {\math{{\cal C}_f}};
\node[below] at (1,0) {1};
\node[left] at (0,1) {1};
\node[below left] at (0,0) {0};

\stopaxis

\stoptikzpicture 

\stoptext