From wiki:
Given a set of independent identically distributed data points $\mathbb{X}=(x_1,\ldots,x_n)$, where $x_i \sim p(x_i|\theta)$ according to some probability distribution parameterized by θ, where θ itself is a random variable described by a distribution, i.e. $\theta > \sim p(\theta|\alpha)$, the marginal likelihood in general asks what the probability $p(\mathbb{X}|\alpha)$ is, where θ has been marginalized out (integrated out):
$$p(\mathbb{X}|\alpha) = \int_\theta p(\mathbb{X}|\theta) \, p(\theta|\alpha)\ \operatorname{d}\!\theta $$
What I don't understand, is integration here. If under p() is random distribution function, as far as I understand it should come just to Bayes formula: $p(\mathbb{X}|\theta) \, p(\theta|\alpha)$.