\begin{tikzpicture}[x=1cm,y=1cm]
  \definecolor{darkergreen}{rgb}{.1,.4,0}
  \definecolor{darkergreen2}{rgb}{.1,.3,0}
  \definecolor{darkeryellow}{rgb}{.4,.4,0}
  \definecolor{lightgreen}{rgb}{.4,.7,.2}
  \definecolor{lightergreen}{rgb}{.5,.8,.3}
  \definecolor{lightyellow}{rgb}{.8,.8,.3}
  \def\ax{-.2} \def\ay{.5}
  \def\bx{.6} \def\by{1.5}
  \def\cx{2.4} \def\cy{-1.1}
  \def\dx{3.4} \def\dy{.9}
  \def\ex{5} \def\ey{-.9}
  \def\fx{5.6} \def\fy{.8}

  % oppervlaktes
  \begin{scope}
    \clip (0,0) rectangle (5.6,1.7);
    \fill[lightgreen]
      (\bx,0) -- (\bx,\by)
      .. controls (\bx+.6,\by) and (\cx-.35,\cy) .. (\cx,\cy)
      .. controls (\cx+.5,\cy) and (\dx-.5,\dy) .. (\dx,\dy)
      .. controls (\dx+.5,\dy) and (\ex-.5,\ey) .. (\ex,\ey)
      -- (\ex,0) -- cycle;
  \end{scope}
  \begin{scope}
    \clip (0,0) rectangle (5.6,-1.2);
    \fill[lightyellow]
      (\bx,0) -- (\bx,\by)
      .. controls (\bx+.6,\by) and (\cx-.35,\cy) .. (\cx,\cy)
      .. controls (\cx+.5,\cy) and (\dx-.5,\dy) .. (\dx,\dy)
      .. controls (\dx+.5,\dy) and (\ex-.5,\ey) .. (\ex,\ey)
      -- (\ex,0) -- cycle;
  \end{scope}

  % hulplijnen
  \draw[darkergreen] (\bx,0) -- (\bx,\by);
  \draw[darkeryellow] (\ex,0) -- (\ex,\ey);
  \node[below=-1] at (\bx,0) {\small $a$\strut};
  \node[above=-1] at (\ex,0) {\small $b$\strut};
  \node at (\bx+.45,.35) {\small $S_1$};
  \node at (\cx,-.35) {\small $S_2$};
  \node at (\dx+.1,.35) {\small $S_3$};
  \node at (\ex-.22,-.35) {\small $S_4$};

  % functie
  \draw[functionstyle,darkblue] (\ax,\ay)
    .. controls (\ax+.3,\ay+.6) and (\bx-.3,\by) .. (\bx,\by)
    .. controls (\bx+.6,\by) and (\cx-.35,\cy) .. (\cx,\cy)
    .. controls (\cx+.5,\cy) and (\dx-.5,\dy) .. (\dx,\dy)
    .. controls (\dx+.5,\dy) and (\ex-.5,\ey) .. (\ex,\ey)
    .. controls (\ex+.2,\ey) and (\fx-.2,\fy-1) .. (\fx,\fy);
  \node[darkblue] at (\fx,\fy) [above] {\small $f(x)$};

  % assen
  \draw[-stealth] (-.5,0) -- (6,0) node[below] {\small $x$};
  \draw[-stealth] (0,-1.5) -- (0,2) node[left=-2] {\small $y$};
\end{tikzpicture}