Meaning of $dF(z)$ in expected utility framework
Not all cdf’s have a density function, (for example if $F$ is not differentiable). However, when they do have a density, the notation $dF(z)$ is equivalent to $f(z)dz$. When performing integrals. However, even if the density does not exists, you can still write the expectation using the notation $dF(z)$. The details of what it actually means and the subtle differences can be learned in any measure theory course. But hopefully this short explanation helps you not freak out every time you see that notation.