reserve A for non empty closed_interval Subset of REAL;

theorem Lm2:
  (id REAL) is_integrable_on A & (id REAL) | A is bounded
proof
  reconsider iR = id REAL as PartFunc of REAL,REAL;
  B1: iR | A is continuous;
  A c= dom iR;
  hence thesis by INTEGRA5:11,INTEGRA5:10,B1;
end;
