the first part of the solution finds C

by using the property that the integral on the density function equals 1

the problem starts in the second part of the question

i need to find the distribution function of Y

where Y=||x|-1|

(my problem i written bellow the photo)

for y<0 we have no graph so the probability is 0.

but when its from zero to 1 it touches four points

i dont know how they got the integral from that fact?

the same goes for when y>1

what is the logic?