.. 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 can you do it now??
Take a look at your graph. The integral is the total area between the function and the x axis. (Areas under the x axis count as negative.) As your function is composed of sections of straight lines, your areas are triangles. Easy to find the area of these.