You don’t. You would have to keep your new page in sync with the core file each time WordPress is updated … that would not be very pragmatic.
Hook into the do_settings_sections('general'); with register_setting() and add your code here.
There is a third parameter for register_setting(): you can register a callback function here which used before the value is saved to the database.
See the @Otto’s WordPress Settings API Tutorial for some examples. In one of my own plugins I do the same: Public Contact Data. See the method function add_contact_fields() for details.