Since random numbers are generated for the uniform distribution \( p(x) \) with \( x\in [0,1] \), we need to perform a change of variables \( x\rightarrow y \) through $$ \begin{equation*} x(y)=\int_a^y p(y')dy', \end{equation*} $$ where we used $$ \begin{equation*} p(x)dx=dx=p(y)dy. \end{equation*} $$ If we can invert \( x(y) \), we find \( y(x) \) as well.