Try this...

Data Range
A
B
C
D
E
F
G
1
Name
Open Date
Register Date
-----
From
To
Total
2
Bob
1/20/2016
1/20/2016
0
0
2
3
Jan
1/1/2016
2/28/2016
1
30
1
4
Dave
2/10/2016
5/1/2016
31
60
1
5
Larry
1/31/2016
8/1/2016
61
90
1
6
Moe
4/1/2016
4/1/2016
91
>91
1
7
Curly
2/5/2016
2/7/2016


This formula entered in G2 and copied down:

=SUMPRODUCT(--(DATEDIF(B$2:B$7,C$2:C$7,"d")>=E2),--(DATEDIF(B$2:B$7,C$2:C$7,"d")<=F2))