\begin{frame}
  \frametitle{Area Between Curves}
  
  \begin{alertblock}{}
    What if we want the area between the curve and the $x$-axis?
  \end{alertblock}\smallskip
  \begin{center}
  \scalebox{.9}{
  \begin{tikzpicture}[default]
    \def\mfun{(-.9 + (\x-3+\mfunshift)^2 - .1*(\x-3+\mfunshift)^4)}

    \diagram[1]{-.5}{6}{-1}{1.7}{1}
    \diagramannotatez
    \def\mfunshift{0}
    \begin{scope}[ultra thick]
      \draw[fill=cgreen,draw=none,opacity=.5] plot[smooth,domain=.5:2,samples=100] (\x,{\mfun}) -- (.5,0) -- cycle;
      \draw[fill=cgreen,draw=none,opacity=.5] plot[smooth,domain=2:4,samples=100] (\x,{\mfun}) -- cycle;
      \draw[fill=cgreen,draw=none,opacity=.5] plot[smooth,domain=4:5.5,samples=100] (\x,{\mfun}) -- (5.5,0) -- cycle;
      \draw[cred] plot[smooth,domain=.5:5.5,samples=100] (\x,{\mfun});
      \node[anchor=north] at (.5,0) {$a$};
      \node[anchor=north] at (5.5,0) {$b$};
      \node[scale=1.8] at (.9,.5) {+};
      \node at (.9,.9) {$A_1$};
      \node[scale=1.8] at (5.15,.5) {+};
      \node at (5.15,.9) {$A_3$};
      \node[scale=1.8] at (3,-.6) {+};
      \node at (3,-.25) {$A_2$};
      \draw[gray] (2,.2) -- node[at end,below,black] {$x_1$} (2,-.2);
      \draw[gray] (4,.2) -- node[at end,below,black] {$x_2$} (4,-.2);
    \end{scope}
  \end{tikzpicture}
  }
  \end{center}\vspace{-.5ex}
  
  \begin{exampleblock}{}
    For example, let us consider the diagram above.
    \medskip
    \pause
    
%     Let $x_1 < x_2$ be the $x$-intercepts.
%     \medskip
%     \pause
%     
    The area between the curve and the $x$-axis from $a$ to $b$ is
    \begin{talign}
      A = \int_a^b |f(x)|dx  \;=\;
      \left| \int_a^{x_1} \!\!\!f(x)\,dx \right| \;+\;
      \left| \int_{x_1}^{x_2} \!\!\!f(x)\,dx \right| \;+\;
      \left| \int_{x_2}^b \!\!\!f(x)\,dx \right| 
    \end{talign}\vspace{-1ex}
    \pause
    
    \alert{Note that we split the integral 
      from $a$ to the first $x$-intercept, from the first to the second $x$-intercept,\ldots}
  \end{exampleblock}
  
  \vspace{10cm}
\end{frame}