I wish to prove the statement in the second paragraph, right after Definition 28.42.1., which goes as follows:
"It is clear that integral/finite morphisms are separated and quasi-compact"
As a first step, I notice that since a morphism is finite if and only if it is of finite type and integral. Therefore we reduce to proving the following statement:
An integral morphism is separated and quasi-compact.
I would appreciate help with the proof that an integral morphism is separated.
Thanks in advance!