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(#)sinh,A) = r*cosh.(upper_bound A) - r*cosh.(lower_bound A)
proof
A1: [#]REAL is open Subset of REAL;
  sinh|A is continuous & sinh|A is bounded by Lm9,Lm14,INTEGRA5:10;
  hence thesis by A1,Lm9,Th31,Th68,INTEGRA5:11,SIN_COS2:35;
end;
