reserve f,f1,f2,g for PartFunc of REAL,REAL;
reserve A for non empty closed_interval Subset of REAL;
reserve p,r,x,x0 for Real;
reserve n for Element of NAT;
reserve Z for open Subset of REAL;

theorem
  integral(r(#)cos,A) = r*sin.(upper_bound A) - r*sin.(lower_bound A)
proof
A1: [#]REAL is open Subset of REAL;
  cos is_integrable_on A & cos|A is bounded by Lm11;
  hence thesis by A1,Th27,Th68,SIN_COS:68;
end;
