Functions of a random variable question

I have this question i cant nut out

f(x)=3/32(4-x^2) when -2<x<2

hence F(x)=0 when -2>x

(3/8)x-(x^3)/32+1/2 when -2<x<2

1 when 2<x

let Y=(X^2)+1, find the CDF of Y

Heres my (probably wrong method or something) working out:

Fy(y)=P(Y<y)=P((x^2+1)<y)=P(X<sqrt(Y-1))=Fx(sqrt(y-1))

therefore Fy(y)=3/8(sqrt(y-1))^(1/2)-((sqrt(y-1))^3)/32+1/2

this isn't a proper CDF when i checked graphing it...

Any help would be appreciated

Edit: yeah, my mistake, i want the CDF of Y