
theorem
for f be PartFunc of REAL,REAL, a,b be Real st a < b & [.a,b.[ c= dom f &
 f is_right_improper_integrable_on a,b &
 abs f is_right_ext_Riemann_integrable_on a,b holds
 max+f is_right_ext_Riemann_integrable_on a,b
proof
    let f be PartFunc of REAL,REAL, a,b be Real;
    assume that
A1:  a < b and
A2:  [.a,b.[ c= dom f and
A3:  f is_right_improper_integrable_on a,b and
A4:  abs f is_right_ext_Riemann_integrable_on a,b;
    f is_right_ext_Riemann_integrable_on a,b by A1,A2,A3,A4,Th57;
    hence thesis by A1,A2,A4,Th64;
end;
