\begin{frame}
  \frametitle{The Definite Integral}

  \begin{exampleblock}{}
    Evaluate the Riemann sum for 
    \begin{talign}
      f(x) = 2x-5
    \end{talign}
    from $0$ to $6$ using $3$ strips and right endpoints as sample points.
    \pause\medskip
    
    We have:
    \begin{itemize}
    \pause
      \item the width of the strips is $\Delta x = \pause (6-0) / 3 \pause = 2$
    \pause
      \item the intervals of the strips are \pause $[0,2]$, $[2,4]$, $[4,6]$
    \pause
      \item the right endpoints are \pause $x_1 = 2$, $x_2=4$, $x_3 = 6$
    \pause
      \item the values at $x_i$'s are \pause $f(x_1) = -1$\pause, $f(x_2) = 3$\pause, $f(x_3) = 7$
    \end{itemize}
    \pause\medskip
    Thus the Riemann sum using $3$ strips and right endpoints is:
    \begin{talign}
      R_3 = \sum_{i=1}^3 f(x_i)\cdot \Delta x = \mpause[1]{2\cdot (-1)} \mpause{+ 2\cdot 3} \mpause{+ 2\cdot 7}
      \mpause{= 18}
    \end{talign}
  \end{exampleblock}
\end{frame}