Returning an array containing values from two passed in arrays
You could offload some of the work to Arrays.copyOf and System.arraycopy:

public static int[] append(int[] first, int[] second) {
  int[] result = Arrays.copyOf(first, first.length + second.length);
  System.arraycopy(second, 0, result, first.length, second.length);
  return result;
}