>The range of x is [-1,1] and y is a function of x, Y=x^2.

>So inputing those values I just get 1 with a multiplicity of 2. I know that doesnt make sense for a range, so clearly im misunderstanding something.

You need to check the values of y = x^2 for all values of x in [-1, 1] - Not just the two end-points.

X ~ U(-1, 1) - So X can take any value in the interval [-1, 1]. This means that Y = X^2 can take any value in the interval [0,1].