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
  A = [.0,1.] implies integral(exp_R,A) = number_e -1
proof
  assume A=[.0,1.];
   then A=[.0,jj.];
  then upper_bound A=1 & lower_bound A=0 by Th37;
  hence thesis by Th53,IRRAT_1:def 7,SIN_COS:51;
end;
