Clear[theta, x, y];
f = 1/(x Cos[theta] + y Sin[theta])^(5/2);
int = Integrate[f, theta];

int /. theta -> 2 Pi

int /. theta -> 0

(int /. theta -> 2 Pi) - (int /. theta -> 0)
(* 0  *)

ClearAll[theta, x, y, f];
f[{x_?NumericQ, y_?NumericQ}, theta_?NumericQ]:= 1/(x Cos[theta]^2+y Sin[theta])^(5/2);

pts = RandomReal[{0, 1}, {5, 2}];(*10 points*)

int = NIntegrate[Evaluate@f[#, theta], {theta, 0, 2 Pi}] & /@ pts