I want to study some topics in machine learning and the author often uses this notation $\mathbb{E}_{x\,\sim\,p(x)}\left[f(x)\right]$. I just wanted to check if this is the same as (for continuous variable $x \in \mathbb{R}$)
$$\mathbb{E}_{x\,\sim\,p(x)}\left[f(x)\right] = \int p(x)f(x)dx.$$
or if this has an additional meaning.