We study density correlation functions for an impenetrable Bose gas in a finite box, with Neumann or Dirichlet boundary conditions in the ground state. We derive the Fredholm minor determinant formulas for the correlation functions. In the thermodynamic limit, we express the correlation functions in terms of solutions of nonlinear differential equations which were introduced by Jimbo, Miwa, Mori, and Sato as a generalization of the fifth Painleve equations.