Help with integral!?

Question

What is the integral of |x^2-1|dx on the interval [0,2]

I'd appreciate any help. Thanks.

Answer 1

|x² - 1| = x² -1 when x² - 1 > 0,
|x² - 1| = 0 when x² - 1 =0, and
|x² - 1| = 1 - x² when x² - 1 < 0.

(The middle one could of course be absorbed into either of the inequalities.)

Divide the integral up into two integrals, one for x from 0 to 1 and one for x from 1 to 2, using the above to write each integrand in the form appropriate for its interval of integration.

Answer 2

same as integral of (0 to 1) -x^2+1 + integral of (1 to 2) x^2-1