theorem :: INTEGR12:27

for n being Element of NAT
for A being non empty closed_interval Subset of REAL
for f being PartFunc of REAL,REAL
for Z being open Subset of REAL st A c= Z & f = (n (#) ((#Z (n - 1)) * sin)) / ((#Z (n + 1)) * cos) & 1 <= n & Z c= dom ((#Z n) * tan) & Z = dom f holds
integral (f,A) = (((#Z n) * tan) . (upper_bound A)) - (((#Z n) * tan) . (lower_bound A))