  We prove necessary optimality conditions of Euler-Lagrange type for
generalized problems of the calculus of variations on time scales with a
Lagrangian depending not only on the independent variable, an unknown function
and its delta derivative, but also on a delta indefinite integral that depends
on the unknown function. Such kind of variational problems were considered by
Euler himself and have been recently investigated in [Methods Appl. Anal. 15
(2008), no. 4, 427-435]. Our results not only provide a generalization to
previous results, but also give some other interesting optimality conditions as
special cases.
