\begin{frame}
  \frametitle{Antiderivatives / Integrals}

  \begin{block}{}
    If $F$ is an antiderivative of $f$ on an interval $I$, \\
    then the \emph{most general antiderivative} of $f$ on $I$ is
    \begin{talign}
      F(x) + C
    \end{talign}
    where $C$ is an arbitrary constant.
  \end{block}
  \pause
  
  \begin{exampleblock}{}
    Find the general antiderivatives of the following functions:
    \begin{itemize}
    \pause
      \item $f(x) = \sin x$\\
            \pause\medskip
            
            $F(x) = \pause -\cos x + C$
    \pause\medskip
      \item $g(x) = x^n$ \quad for $n \ne -1$\\
            \pause\medskip

            $G(x) = \pause \frac{1}{n+1}x^{n+1} + C$
            \pause\medskip
            
            If $n \ge 0$, then this is valid for any interval.
            \\\pause
            If $n < 0$ \& $n \ne -1$, then valid for intervals not containing $0$.
    \end{itemize}
  \end{exampleblock}
\end{frame}