With this change of variables we can express the integral of Eq. (20) as $$ \begin{equation*} I=\int_a^b p(y)\frac{F(y)}{p(y)} dy=\int_{\tilde{a}}^{\tilde{b}}\frac{F(y(x))}{p(y(x))} dx, \end{equation*} $$ meaning that a Monte Carlo evaluation of the above integral gives $$ \begin{equation*} \int_{\tilde{a}}^{\tilde{b}}\frac{F(y(x))}{p(y(x))} dx= \frac{1}{N}\sum_{i=1}^N\frac{F(y(x_i))}{p(y(x_i))}. \end{equation*} $$