The Stacks project

Exercise 111.2.6. Let $A \subset B$ be an integral ring extension. Prove that $\mathop{\mathrm{Spec}}(B) \to \mathop{\mathrm{Spec}}(A)$ is surjective. Use the exercises above, the fact that this holds for a finite ring extension (proved in the lectures), and by proving that $B = \mathop{\mathrm{colim}}\nolimits B_ i$ is a directed colimit of finite extensions $A \subset B_ i$.