Here's an example Java program that adds two integers:

public class AddTwoIntegers {
    public static void main(String[] args) {
        int num1 = 5;
        int num2 = 10;

        int sum = num1 + num2;

        System.out.println("The sum of " + num1 + " and " + num2 + " is " + sum + ".");
    }
}

In this example, we create two integer variables called num1 and num2 and assign them the values 5 and 10, respectively. We then add the two numbers together and store the result in a third variable called sum. Finally, we print out the result to the console using the System.out.println() method.

The output of this program will be:

The sum of 5 and 10 is 15.