
theorem Th20:
for f be PartFunc of REAL,REAL, b be Real
 st f is_-infty_ext_Riemann_integrable_on b
 holds f is_-infty_improper_integrable_on b
proof
    let f be PartFunc of REAL,REAL, b be Real;
    assume
A1:  f is_-infty_ext_Riemann_integrable_on b; then
    ex Intf be PartFunc of REAL,REAL st dom Intf = left_closed_halfline b
     & (for x be Real st x in dom Intf holds Intf.x = integral(f,x,b))
     & Intf is convergent_in-infty by INTEGR10:def 6;
    hence f is_-infty_improper_integrable_on b by A1,INTEGR10:def 6;
end;
