theorem :: INTEGR21:18

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