 reserve h,h1 for 0-convergent non-zero Real_Sequence,
         c,c1 for constant Real_Sequence;

theorem
  for f be PartFunc of REAL,REAL, a,b be Real holds
   integral(f,b,a) = -integral(f,a,b)
proof
    let f be PartFunc of REAL,REAL, a,b be Real;
    per cases;
    suppose a <= b; then
A1:  ['a,b'] = [.a,b.] by INTEGRA5:def 3; then
     integral(f,['a,b']) = integral(f,a,b) by INTEGRA5:19;
     hence integral(f,b,a) = -integral(f,a,b) by A1,INTEGRA5:20;
    end;
    suppose a > b; then
A2:  ['b,a'] = [.b,a.] by INTEGRA5:def 3; then
     -integral(f,['b,a']) = integral(f,a,b) by INTEGRA5:20;
     hence integral(f,b,a) = -integral(f,a,b) by A2,INTEGRA5:19;
    end;
end;
