theorem :: INTEGR14:22

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 = (exp_R * cosec) (#) (cos / (sin ^2)) & Z = dom f & f | A is continuous holds

integral (f,A) = ((- (exp_R * cosec)) . (upper_bound A)) - ((- (exp_R * cosec)) . (lower_bound A))

for f being PartFunc of REAL,REAL

for Z being open Subset of REAL st A c= Z & f = (exp_R * cosec) (#) (cos / (sin ^2)) & Z = dom f & f | A is continuous holds

integral (f,A) = ((- (exp_R * cosec)) . (upper_bound A)) - ((- (exp_R * cosec)) . (lower_bound A))