theorem Th71: :: MESFUN15:69

for f being PartFunc of REAL,REAL
for a, b being Real st ].a,b.] c= dom f & max+ f is_left_ext_Riemann_integrable_on a,b & max- f is_left_ext_Riemann_integrable_on a,b holds
( f is_left_ext_Riemann_integrable_on a,b & left_improper_integral (f,a,b) = (left_improper_integral ((max+ f),a,b)) - (left_improper_integral ((max- f),a,b)) )