theorem Th68: :: INTEGRA8:68

for f being PartFunc of REAL,REAL
for A being non empty closed_interval Subset of REAL
for r being Real
for Z being open Subset of REAL st f is_differentiable_on Z & A c= Z & f `| Z is_integrable_on A & (f `| Z) | A is bounded holds
integral ((r (#) (f `| Z)),A) = (r * (f . (upper_bound A))) - (r * (f . (lower_bound A)))