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Consider the function $B$ defined by the rule $\displaystyle B(x) = \int_1^x f(t)\ dt$ where $f(t) = 6-2t$.
\begin{enumerate}
    \item Compute $B(1)$ and $B(2)$ exactly.
    \item Use the first Fundamental Theorem of Calculus to find a formula for $B(x)$ that does not involve integrals. That is, use the first FTC to evaluate $\displaystyle \int_1^x (6-2t)\ dt$.
    \item Observe that $f$ is a linear function; what kind of function is $B$?
    \item Using the formula that you found in part (b) that does not involve integrals, compute $B'(x)$.
    \item While we have defined $f$ by the rule $f(t) = 6-2t$, it is equivalant to say that $f$ is given by the rule $f(x) = 6-2x$. What do you observe about the relationship between $B$ and $f$?
\end{enumerate}
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