Determining the polar moment of an inertia for a non-uniform circular cross section

Question

I know the integral for determining the polar moment of inertia for a given geometry is given by:

$$J=\iint R^2dA$$

For the attached geometry there is a circular cross section with distinct areas. I was wondering if I can simply the expression as below, my knowledge of integrals has fallen swiftly since leaving uni...

Attached Image

$$J = \sum R_i^2A_i$$