public int Add(string delimiter, string input)
{
    return string.IsNullOrWhiteSpace(input) ?
        0 :
        Sum(delimiter, input);
}

private static int Sum(string delimiter, string input)
{
    var numbers = input
        .Split(new [] {delimiter}, StringSplitOptions.None)
        .Where(ItIsInt)
        .Select(int.Parse);
        .Sum();
}