why is the last formula range from x->1 not from 0->1?

Example 8.22 First, a point Y is selected at random from the interval (0, 1). Then another point X is chosen at random from the interval (0, Y). Find the probability density function of X Solution: Let f (x, y) be the joint probability density function of X and Y. Then fx ( x ) = / f (x.>dy. where from fair (xly) = f (x. y) fr(y) we obtain f ( x, y ) = fxIr ( xly) fr (x). Therefore, fx ( x ) = / fx x (xly ) fy (y )dy. Since Y is uniformly distributed over (0, 1), fr (x ) = 10 if 0 fxx (xly) = elsewhere. Thus fx ( x ) = / fx r (xly)fy(y)dy = In 1 - In x = - Inx. why is it