I have the following step during a proof: https://i.stack.imgur.com/vFHZK.png
$$= \int_{\mathbb{R}} \frac{f(y,z)}{F_Y(y)} dz \\ = \frac{\displaystyle\int_\mathbb{R}f(y,z) \,dz}{F_Y(y)}$$ where f(y,z) is the joint density function of the variables Y and Z. F_Y(y) is the marginal density function of Y. I dont understand why you can bring the integral inside the numerator. Then the denominator doesn't get integrated? Tyvm for any help!
$F_Y(y)$ doesn't depend on $z$ so it's treated like a constant during the integration. The same way we can write: $$\int_\mathbb{R} a f(x) \,dx = a \int_\mathbb{R} f(x)\, dx$$ we can also write $$\int_{\mathbb{R}} \frac{f(y,z)}{F_Y(y)} dz =\frac{1}{F_Y(y)}\int_\mathbb{R}f(y,z) \,dz = \frac{\displaystyle\int_\mathbb{R}f(y,z) \,dz}{F_Y(y)}$$