\begin{frame} \frametitle{Fundamental Theorem of Calculus} \begin{block}{Fundamental Theorem of Calculus} Suppose $f$ is a continuous function on $[a,b]$. Then \begin{enumerate} \pause \item If \vspace{-1ex} \begin{talign} g(x) = \int_a^x f(t)dt\, \end{talign} \vspace{-1ex} then $g'(x) = f(x)$. \medskip\pause \item Let $F$ be any antiderivative of $f$, that is, $F' = f$. Then \begin{talign} \int_a^b f(x)dx = F(b) - F(a) \end{talign} \end{enumerate} \end{block} \pause\medskip The first part of the theorem can be written as:\vspace{-1ex} \begin{talign} \frac{d}{dx} \int_a^x f(t)dt = f(x) \end{talign} \pause The second part can be written as:\vspace{-1ex} \begin{talign} \int_a^b F'(x)dx = F(b) - F(a) \end{talign} \end{frame}