Find the area of the region under the graph of $f$ on $[ a , b ]$.
$$f ( x ) = x ^ { 2 } - 2 x + 2 ; \quad [ - 1,2 ]$$
A) $- 3$
B) $- 6$
C) 6
d 3

Question

Quizplus · Accepted Answer

The area under the graph of a function between two endpoints can be found by integrating the function over that interval. 
$$\int_{a}^{b} f(x) dx = \int_{-1}^{2} (x^2 - 2x + 2) dx = \left[ \frac{x^3}{3} - x^2 + 2x \right]_{-1}^{2} = \frac{8}{3} - 4 + 4 + \frac{1}{3} + 1 - 2 = 6$$
Therefore, the area under the graph of $f$ on $[a,b]$ is 6, making the answer choice C.

Find the Area of the Region Under the Graph Of f