Please consider Example 4.8 on <http://www.probabilitycourse.com/chapter4/4_1_3_functions_continuous_var.php>

Would someone mind explaining how $P(X^2≤y)=P(−\sqrt{y}≤X≤\sqrt{y})$ and how $R\_y=[0,1]$ (essentially if $-1<x<1$ how does it become $0<y<1$)?

Thanks.