I am working on solving the Biot-Savart Law equation for the magnetic field around a charged ring of uniform current density. The expression that Mathematica gives is rather nasty, as expected. Notice that the limits of integration are not included in the solution. Mathematica rejects the bounds of integration by silently refusing to even consider a solution (literally, it sits there for several minutes "Running..." and then just stops like nothing ever happened). My idea was that since Mathematica didn't mind handing over the indefinite integral, that I could turn it into a function of theta and manually apply the first fundamental theorem of calculus. For some reason, I can't seem to convince Mathematica that I want this to be a function that I want evaluated at 2Pi and at 0 so that they can be subtracted. Here is the code up to the integration. Thanks in advance for any feedback.

s=1;

m=4*Pi*10^7;

l[Theta_]:={s Cos[Theta],s Sin[Theta],0};

R={x,y,z}-l[Theta];

r=R/Sqrt[R.R];

Deel=D[l[Theta],Theta];

Cross[Deel,r];

Integrand=%/R.R;

B=(m/4*Pi) Integrate[(Integrand),Theta,GenerateConditions ->False]