Barrons AP Calculus

Figure  N6–11a

Figure  N6–11b

All that remains is to evaluate f(x) at x = 1, 2, and 3. We use the Fundamental
Theorem of Calculus to accomplish this, finding f also at x = 4 and 5 for
completeness.
We are given that f(0) = 1. Then

where the integral yields the area of the triangle with height 2 and base 1;

where the integral gives the area of a quadrant of a circle of radius 1 (this
integral is negative!);