\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) {$A_2$};
    \end{scope}
  \end{tikzpicture}
  }
  \end{center}\vspace{-.5ex}

  \begin{block}{}
    Let $f$ be continuous on $[a,b]$.
    \medskip
    
    Then the area between the curve $f$ and the $x$-axis from $a$ to $b$ is
    \begin{talign}
      A = \int_a^b |f(x)|dx 
    \end{talign}
  \end{block}
  \pause
  
  \alert{To evaluate the integral, we split the it into $A_1$, $A_2$ and $A_3$.}\\
  \pause Thus we must find the $x$-intercepts in $[a,b]$!
  \vspace{10cm}
\end{frame}