Flux through arc of circle

I have to compute a magnetic flux though an arc.
I tried to specify a parametrized curve 2D to evaluate the integration but I do not know how to specify the minimum and the maximum value of the parametrization implicitly through a parameter (e.g. d1/5)

I have to compute this simulation for several different d1 by matlab...
Do you suggest me to modify the .m code or it would be the same?