How do I rearrange $E[\log p(X, Y|\Theta)|X, \Theta^{(i - 1)}]$ to $\int_{y \in \Upsilon} \log p(X, y|\Theta)f(y|X, \Theta^{(i - 1)})dy$?

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Equation (2) from here. Is there a formula for this? Also what does it mean if only the bottom part of the integral is specified, and how does $y \in \Upsilon$ even work in an integral?

Thanks in advance.