# Uniqueness of Stein factorization

Let $$X \overset{f^\prime}\longrightarrow S^\prime \overset\pi\longrightarrow S$$ be morphisms of schemes such that $$f^\prime$$ is proper with geometrically connected fibers and $$\pi$$ is integral. Set $$f = \pi \circ f^\prime$$. Is it true that $$S^\prime$$ is the normalization of $$S$$ in $$X$$.

No. Take $$S=S’$$ a cuspidal curve, $$\pi$$ the identity, and $$f’=f: X\to S’=S$$ the normalization.