Originally Posted by

**evansf** Given

first sketch the graph

*y *= *f(x) *on the given interval. Then find the integral of *f *using your knowledge of area formulas for

rectangles, triangles and circles.

.. now, this can be separated to

..

we know, in the first addend, x is negative, hence we take |x| = -x; on the other hand, in the second addend, x is positive hence |x| = x

so the integral would be

now, we have to check where |1-x| is positive or negative and |1+x| is positive or negative..

for |1-x|, we take 1-x if 1-x >= 0 or x <= 1; we take x-1 otherwise

for |1+x|, we take 1+x if 1+x >= 0 or x >= -1; we take -x-1 otherwise

so now,

so can you do it now??