I am reading the Deep Learning book and having some difficulties with the following formula (page 134):

$$ p(X^{m+1} | x^1, \dots, x^m) = \int p(X^{m+1} | \theta) p(\theta | x^1, \dots, x^m) d\theta. $$

Intuitively, it just makes sense: we simply compute the probability of observing the point $m+1$ given the parameters, times the probability of having that parameter given the previous observations. And we integrate over theta because of its uncertainty. Nonetheless, I do not know how to actually derive this formula from other probability rules. Is this just intuition or is there a formal derivation? Thank you.

I'm self-studying it, so I'm not asking for help on assignments. Nonetheless, if there is a derivation, I'd like to have just an hint.