theorem Th17: :: INTEGR25:17

for f being PartFunc of REAL,REAL
for a, b being Real st a <= b & left_closed_halfline b c= dom f & f is_integrable_on ['a,b'] & f | ['a,b'] is bounded & f is_-infty_ext_Riemann_integrable_on a holds
( f is_-infty_ext_Riemann_integrable_on b & infty_ext_left_integral (f,b) = (infty_ext_left_integral (f,a)) + (integral (f,a,b)) )