How do you find the integral of #x^2-6x+5# from the interval [0,3]?
We can use the reverse power rule:
This is equivalent to:
Therefore, the answer is -3. Note that the definite integral gives the net area under the graph. The negative sign implies that there is more area below the x-axis (than above) for the interval from 0 to 3 (inclusive).
If you are unfamiliar with the reverse power rule, this might help: https://www.khanacademy.org/math/ap-calculus-ab/ab-antiderivatives-ftc/ab-reverse-power-rule/v/indefinite-integrals-of-x-raised-to-a-power