Velocity Profile Integral

This is more of a physics question, but I'm not understanding the mathematical side which is why I'm putting it in this forum.

I've attached the question and answer to the post. In the question, it states that the radius of the cylinder is R, and the radial distance is r. What is the difference between these two? My other problem is with how they are integrating. As they have said, mass flow rate = $\rho \bar{U}A=\int \rho \bar{U} AdA$. Using $dA=rdrd\theta$ they've put it into a double integral... but the A seems to have disappeared. Surely the new integral should be $\int \int \rho \bar{U} \pi r^2drd\theta$?

R is the radius if the cylinder, a constant, whereas r is the radial distance of a point within the cylinder.

There shouldn't be an A in the integral as the area of a shape is

$A = \int \int dA$