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\noindent {\bf Problem statement} The graph of $f$ is shown to the
right.  The function $F(x)$ is defined by $F(x)=\int_0^x f(t)\, dt$
for $0\le x\le 4$.

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\noindent a) Find $F(0)$ and $F(3)$.

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\noindent b) Find $F'(1)$.

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\noindent c) For what value of $x$ does $F(x)$ have its maximum value?
What is this maximum value?

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