
theorem Th21:
for f be PartFunc of REAL,REAL, a be Real
 st f is_+infty_ext_Riemann_integrable_on a
 holds f is_+infty_improper_integrable_on a
proof
    let f be PartFunc of REAL,REAL, a be Real;
    assume
A1:  f is_+infty_ext_Riemann_integrable_on a; then
    ex Intf be PartFunc of REAL,REAL st dom Intf = right_closed_halfline a
     & (for x be Real st x in dom Intf holds Intf.x = integral(f,a,x))
     & Intf is convergent_in+infty by INTEGR10:def 5;
    hence f is_+infty_improper_integrable_on a by A1,INTEGR10:def 5;
end;
