theorem Th63: :: INTEGR24:63

for f, g being PartFunc of REAL,REAL
for a, b being Real st ].a,b.[ c= dom f & ].a,b.[ c= dom g & f is_improper_integrable_on a,b & g is_improper_integrable_on a,b & ( not improper_integral (f,a,b) = +infty or not improper_integral (g,a,b) = -infty ) & ( not improper_integral (f,a,b) = -infty or not improper_integral (g,a,b) = +infty ) holds
( f + g is_improper_integrable_on a,b & improper_integral ((f + g),a,b) = (improper_integral (f,a,b)) + (improper_integral (g,a,b)) )