theorem :: INTEGR18:15

for X being RealNormSpace
for A being non empty closed_interval Subset of REAL
for f1, f2 being PartFunc of REAL, the carrier of X st f1 is_integrable_on A & f2 is_integrable_on A & A c= dom f1 & A c= dom f2 holds
( f1 - f2 is_integrable_on A & integral ((f1 - f2),A) = (integral (f1,A)) - (integral (f2,A)) )