Real-world problems are often nonconvex and involve integer variables, representing vexing challenges to be tackled using state-of-the-art solvers. We introduce a mathematical identity-based reformulation of a class of polynomial integer nonlinear optimization (PINLO) problems using a technique that linearizes polynomial functions of separable and bounded integer variables of any degree. We also introduce an alternative reformulation and conduct computational experiments to understand their performance against leading commercial global optimization solvers. Computational experiments reveal that our integer linear optimization (ILO) reformulations are computationally tractable for solving large PINLO problems via Gurobi (up to 10,000 constraints and 20,000 variables). This is much larger than current leading commercial global optimization solvers such as BARON, thereby demonstrating its promise for use in real-world applications of integer linear optimization with a polynomial objective function.