calculating a flux through a curved surface

Hi,
I working on solving the electrokinetics problem in the attached geometry.
I solve the problem but I am having problems with post-processing.

I am interested in calculating the flux through the left semi-circular lobe.

For simplicity lets assume we have one species.

Obviously the flux has an x and y component ( jx and jy).
I have tried using line integration of the total normal flux offered by Comsol but I got the incorrect solution.

I tried to simplify the problem by understanding how line integration works and I get a weird result.
So when I did line integration of 1 on the left semi-circular lobe I simply got pi/2*R which makes sense.
When I integrated x on the lobe I got R^2. This doesn't make sense... I have not been able to fully understand how the line integration function works?

What command should I type in to get the total flux through ?

jx*ny+jy*nx

(nx and ny are the normal vectors to the geometry)

Thanks,