Generating random numbers with specific probability distribution function

Random variable x has the probability distribution function (PDF):

• f(x) = 1/2 for x ~ [-1, 1].
• f(x) = 0 for x ~ (-inf, 0) (1, inf).

Random variable y is defined as y = x2.

What is the PDF of y in that case? How can I generate (pseudo) random numbers that follow the distribution of x, using the equation given for y, plotting the histogram of y?