theorem :: INTEGR11:34

for A being non empty closed_interval Subset of REAL
for Z being open Subset of REAL
for f being PartFunc of REAL,REAL st A c= Z & f = #Z 2 & Z = dom ((1 / 2) (#) f) holds
integral ((id Z),A) = (((1 / 2) (#) f) . (upper_bound A)) - (((1 / 2) (#) f) . (lower_bound A))