Let $R\subset S$ be domains such that $S$ is a finitely generated $R$-algebra. Show that there exists $f\in R$, $f\neq0$, and elements $y_1,\dots,y_r\in S$ algebraically independent over $R$ such that $S_f$ is integral over $S'_{f}$, where $S'=R[y_1,\dots,y_r]$.
I am trying to prove it via Noether's normalization lemma; but I am not able to solve this problem, despite various attempts. Any help or hints will be appreciated. Thanks in advance.