reserve A for non empty closed_interval Subset of REAL;

theorem Th17B:
for a,b being Real holds
AffineMap (a,b) | A is bounded & AffineMap (a,b) is_integrable_on A
proof
 let a,b be Real;
 reconsider f = AffineMap (a,b) as PartFunc of REAL,REAL;
 A c= REAL; then
 A1: A c= dom f by FUNCT_2:def 1;
 f | A is continuous;
 hence thesis by INTEGRA5:11,INTEGRA5:10,A1;
end;
