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\begin{frame}
  \frametitle{The Area below a Curve}

  \begin{alertblock}{}
  How to compute the area below a curve?
  \end{alertblock}
  \medskip
  
  \begin{center}
  \scalebox{.8}{
  \begin{tikzpicture}[default]
    \def\mfun{(4*((\x+\mfunshift)/4)^2)}

    \diagram[1]{-.5}{4.5}{-.4}{4.5}{1}
    \diagramannotatez
    \diagramannotatexx{1/.25,2/.5,3/.75,4/1}
    \diagramannotateyy{1/.25,2/.5,3/.75,4/1}
    \def\mfunshift{0}
    \begin{scope}[ultra thick]
      \draw[cred] plot[smooth,domain=0:4,samples=20] (\x,{\mfun});
      \draw[draw=none,fill=cred,opacity=.5] (.5,0) -- plot[smooth,domain=0:4,samples=20] (\x,{\mfun}) -- (4,0) -- (0,0) -- cycle;
    \end{scope}
  \end{tikzpicture}
  }
  \end{center}
  \pause
    
  \begin{exampleblock}{}
    Idea: 
    \begin{itemize}
    \pause
      \item divide the area in vertical strips of equal width
    \pause
      \item approximate the area using rectangles
    \end{itemize}
  \end{exampleblock}

  \vspace{10cm}
\end{frame}