Consider the function $A$ defined by the rule $$A(x) = \int_1^x f(t) \, dt,$$ where $f(t) = 4-2t$.

Compute $A(1)$ and $A(2)$ exactly.
$A(1)=$
$A(2)=$

Use the First Fundamental Theorem of Calculus to find an equivalent formula for $A(x)$ that does not involve integrals. That is, use the first FTC to evaluate $\int_1^x (4-2t) \, dt$.
$A(x)=$

Observe that $f$ is a linear function; what kind of function is $A$?
Answer: ? Linear Quadratic Cubic Tigonometric Non-Algebraic

Using the formula you found above for $A(x)$, that does not involve integrals, to compute $A'(x)$.
$A'(x) =$

While we have defined $f$ by the rule $f(t) = 4-2t$, it is equivalent to say that $f$ is given by the rule $f(x) = 4 - 2x$. What do you observe about the relationship between $A$ and $f$?