Section 2.2.7 of "Machine Learning: A Probabilistic Perspective of Kevin Patrick Murphy" gives this formula for the expected value.

$ { displaystyle operatorname {E} (X) = int _ { mathbb {X}} xf (x) , dx.} $

there is an X at the bottom of the integral symbol. What is it? `X`

do you mean here? Does it mean "the domain of the definition", "support" or something else?