\begin{frame}
  \frametitle{Fundamental Theorem of Calculus}
  
  \vspace{-3ex}
  \begin{talign}
    g(x) = \int_a^x f(t)dt &&\implies&& g'(x) = f(x)
  \end{talign} \vspace{-1ex}
  \pause
  
  \scalebox{.8}{
  \begin{tikzpicture}[default]
    \diagram[1]{-1}{4}{-0}{6.5}{1}
    \diagramannotatez
    \diagramannotatex{1,2,3}
    \diagramannotatey{1,2,3,3}
    \node[cred] at (2,6.5) {$f(x)$};
    
    \draw[cred] plot[smooth,domain=-1:1.5,samples=20] (\x,{1});
    \draw[cred] plot[smooth,domain=1.5:2.5,samples=20] (\x,{2});
    \draw[cred] plot[smooth,domain=2.5:3.5,samples=20] (\x,{3});

    \onslide<3->{ \draw[draw=none,fill=cred,opacity=.5] plot[ybar interval,domain=0.5:1.5,samples=2] (\x,{1}); }
    \onslide<4->{ \draw[draw=none,fill=cred,opacity=.5] plot[ybar interval,domain=1.5:2.5,samples=2] (\x,{2}); }
    \onslide<5>{ \draw[draw=none,fill=cred,opacity=.5] plot[ybar interval,domain=2.5:3.5,samples=2] (\x,{3}); }

    \onslide<6->{ 
      \draw[draw=none,fill=cred,opacity=.5] plot[ybar interval,domain=2.5:3,samples=2] (\x,{3}); 
      \draw[dashed,cblue] (3,-.5) -- node [at end,above] {$x = 3$} (3,6.5);
      \node at (1.75,.5) {area = $4.5$};
    }
      
    \begin{scope}[xshift=.65\textwidth]
      \diagram[1]{-1}{4}{-0}{6.5}{1}
      \diagramannotatez
      \diagramannotatex{1,2,3}
      \diagramannotatey{1,2,3,4,5,6}
      \node[cred] at (2,6.5) {$g(x) = \int_{0.5}^x f(t)\,dt$};

      \pause
      \node[cred,include] at (1.5,1) {};
      \draw[cred] plot[smooth,domain=0.5:1.5,samples=20] (\x,{\x-.5});
      \pause
      \node[cred,include] at (2.5,3) {};
      \draw[cred] plot[smooth,domain=1.5:2.5,samples=20] (\x,{2*\x-2});
      \pause
      \node[cred,include] at (3.5,6) {};
      \draw[cred] plot[smooth,domain=2.5:3.5,samples=20] (\x,{3*\x-4.5});

      \pause
      \node[include,cblue] at (3,4.5) {};
      \draw[dashed,cblue] (3,-.5) -- (3,6.5); % node [at end,above] {$x = 3$}
    \end{scope}
    
    \begin{scope}[line width=2mm,cgreen,->,xshift=.5cm]
    \onslide<7->{ 
      \draw[opacity=.7] (1.5,1) to[bend left=23] (9,4.3);
      \path[decoration={text along path,raise=2mm,text={area = integral\ \ \ \ \ \ },text align={center}},decorate] (1.5,1) to[bend left=23] (9,4.3);
    }
    \onslide<8->{ 
      \draw[opacity=.7] (9,4.9) to[bend left=-25] (2.9,3.4);
      \path[decoration={text along path,raise=2mm,text={slope = derivative\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ },text align={center}},decorate] (2.9,3.4) to[bend left=25] (9,4.9);
    }
    \end{scope}
    \pause
    \pause
    \pause
  \end{tikzpicture}
  }\smallskip
  
  \mpause[0]{
  Observe: $g'(x) = f(x)$ except where $f$ is not continuous.\vspace{-.75ex}
  }
  \mpause[1]{
  \begin{alertblock}{}
    The slope (derivative) is the inverse of taking the area (integral).
  \end{alertblock}
  }
  \vspace{10cm}
\end{frame}