declare @t table(id int identity(1,1),begindate datetime,enddate datetime)

insert @t select '2007-1-1','2007-1-10'
union all select '2007-1-3','2007-1-20'
union all select '2007-2-1 ','2007-2-10'


select 
    sum(datediff(day,a.begindate,case when a.enddate > b.begindate then b.begindate else a.enddate end)) as diffday
from @t a
outer apply(
    select begindate
    from @t
    where id = a.id + 1)b