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Consider the continuous function $f$ sketched below:
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\begin{enumerate}[(a)]
\item Is $\displaystyle{\int_{1}^{0}f(t)\ dt}$ positive, zero, or negative?  Give reasons for your answer.
\item Is $\displaystyle{\int_{1}^{3}f(t)\ dt}$ larger or smaller than $\displaystyle{\int_{1}^{0}f(t)\ dt}$?  Give reasons for your answer.
\item Is $\displaystyle{\int_{1}^{4}f(t)\ dt}$ larger or smaller than $\displaystyle{\int_{1}^{3}f(t)\ dt}$?  Give reasons for your answer.
\item Where do the local maximums and local minimums of the function $\displaystyle{F(x)=\int_{1}^{x}f(t)\ dt}$ occur?  Give reasons for your answer.
\item Estimate the intervals where the graph of $F(x)$ is concave up and and where the graph of $F(x)$ is concave down.
\item Let $\displaystyle{G(x)=\int_{0}^{x}f(t)\ dt}$.  How would you answer parts (d) and (e) for $G(x)$?  Explain.
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