\begin{frame} \frametitle{Antiderivatives / Integrals} \begin{block}{} A function $F$ is called \emph{antiderivative} of $f$ on an interval $I$ \\ if $F'(x) = f(x)$ for all $x$ in $I$. \end{block} \pause \begin{exampleblock}{} Let $f(x) = x^2$ then an antiderivative of $f$ is \begin{talign} F(x) = \mpause[1]{\frac{1}{3}x^3} \end{talign} \pause\pause However $f$ has more antiderivatives; every function of the form \begin{talign} G(x) = \mpause[1]{\frac{1}{3}x^3 + C \quad\quad \text{where $C$ is a constant}} \end{talign} \pause\pause Can there be other antiderivatives? \pause No! by next theorem\ldots \end{exampleblock} \end{frame}