Graph of [math]

The blue line in the graph above defines a linear function [math].
(A) Suppose that [math] is a point that may vary on the [math]-axis. Find the accumulated area function [math] that calculates the net area of the shaded region on the interval [math]. Hint: What is the area of a triangle?
[math]

(B) Find the antiderivative for the function [math] that has constant term zero.
Antiderivative [math]

(C) The functions [math] and [math] are both antiderivatives of [math].

Solution: