The blue line in the graph above defines a linear function $y = f(t)$.
(A) Suppose that $x > 5$ is a point that may vary on the $t$-axis. Find the accumulated area function $$A(x) = \int_0^x f(t) \, dt$$ that calculates the net area of the shaded region on the interval $\lbrack 0, x \rbrack$. Hint: What is the area of a triangle?
$A(x) =$

(B) Find the antiderivative for the function $f(t)$ that has constant term zero.
Antiderivative $F(t) =$

(C) ? True False The functions $A$ and $F$ are both antiderivatives of $f$.

Solution: