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(sinh(#)sinh,A)=cosh.(upper_bound A)*sinh.(upper_bound A)-
  cosh.(lower_bound A)*sinh.(lower_bound A)-integral((cosh)(#)(cosh),A)
proof
A1: [#]REAL is open Subset of REAL;
A2: sinh`|REAL is_integrable_on A & (sinh`|REAL)|A is bounded by Lm17,Th30;
  (cosh)`|REAL is_integrable_on A & (cosh`|REAL)|A is bounded by Lm15,Th31;
  hence thesis by A2,A1,Th30,Th31,INTEGRA5:21,SIN_COS2:34,35;
end;
