jmc

The rectangular region is 10 units by 8 units, resulting in an 8 by 6 rectangular region in the interior, which forms a 9-by-7 array of lattice points. That's $\boxed{63}$ points with integer coordinates, as shown in the figure. Note: We are counting points, not squares. It is a common mistake to count the interior squares, for 48, instead of interior lattice points, which gives the correct answer of 63.