This is just a demo website, but in a real use case you would pass a context (for instance with the user timezone, country...) with your library calls.

You can also try the same sentence in French, you'll get February first.

Are there countries that use slashes for d/m/y?

What surprised me was "1-2-2014":

  From Thursday, 2 October 2014 at 1:02:00 +0000 (UTC)
  to Wednesday, 1 January 2014 at 0:00:00 +0000 (UTC)

On top of the "where did it get those timestamps from", time flows backwards in that interval.