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\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}