theorem :: INTEGR21:16

for a, b, c, d being Real
for Y being RealBanachSpace
for f, g being continuous PartFunc of REAL, the carrier of Y st a <= c & c <= d & d <= b & ['a,b'] c= dom f & ['a,b'] c= dom g holds
( f + g is_integrable_on ['c,d'] & (f + g) | ['c,d'] is bounded )