How to find Sum of # of days w/o counting overlapping days twice

Yes this is interesting and challenging. Arrived at a different approach.

Row\Col	A	B	C	D	E
1	Start	End
2	**1/6/2015	1/10/2015	0	0	Array-entered C2 : {=SUM(IF(FREQUENCY(ROW(INDIRECT($A2&":"&$B2)),IFERROR(ROW(INDIRECT($A1&":"&$B1)),0))=1,1,0))+$C1}
3	**1/13/2015	1/20/2015	0	0	D2 : =SUM($C$2:$C2)
4	**1/12/2015	1/22/2015	7	7
5	**1/18/2015	1/25/2015	12	19