for f, Intf being PartFunc of REAL,REAL
for b being Real st f is_-infty_improper_integrable_on b & dom Intf = left_closed_halfline b & ( for x being Real st x in dom Intf holds
Intf . x = integral (f,x,b) ) & Intf is convergent_in-infty holds
improper_integral_-infty (f,b) = lim_in-infty Intf