Calculate minimum of two independent and Multidisciplinary function random variable

I want to calculate CDF of Y, when Y=min{X1,X2} and X is Multidisciplinary function. (FX = B(x) when 1 < x < A) and (FX = D(x) when A < x < A^2). I know that FY=1-((1-FX)^2). but it doesn't work when X is multidisciplinary function. How can I calculate FY?