Calculate total duration from a set of dates excluding overlapping days

Calculate total duration from a set of dates excluding overlapping days

Given a set of dates, what's the best method to get the total duration
excluding overlapping days?
For example:
Start Date End Date
10/08/2013 15/08/2013
13/08/2013 16/08/2013
09/08/2013 12/08/2013
29/08/2013 30/08/2013
08/08/2013 17/08/2013
Duration is 10 days