reserve A for non empty closed_interval Subset of REAL;

theorem
for a,b be Real holds
(id REAL) is_integrable_on ['a,b'] & (id REAL) | ['a,b'] is bounded
proof
 let a,b be Real;
 reconsider iR = (id REAL) as PartFunc of REAL,REAL;
 B1: iR | ['a,b'] is continuous;
 ['a,b'] c= dom iR;
 hence thesis by INTEGRA5:11,INTEGRA5:10,B1;
end;
