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

  \begin{block}{}
  If the limit
  \begin{talign}
    \int_{a}^{b} f(x)dx = \lim_{n\to \infty} \sum_{i = 1}^n f(x_i) \Delta x
  \end{talign}
  exists, then $f$ is called \emph{integrable} on $[a,b]$.
  \end{block}
  \pause\bigskip
  
  Note every function is integrable.
  
  \pause\bigskip
  However, most of the functions we work with are:
  \pause
  \begin{block}{}
    If 
    \begin{itemize}
      \item $f$ is continuous on $[a,b]$, or
      \item $f$ has only a finite number of jump discontinuities,
    \end{itemize}
    then $f$ is integrable on $[a,b]$,
    that is, the $\int_{a}^{b} f(x)dx$ exist.
  \end{block}
  \vspace{10cm}
\end{frame}