How to get the values by using BETWEEN AND Operator

Question

Hi Everyone,
I want to get the date from table so i used between and operator, it's working but it should get only in-between dates.... I want to get the from date till to date....Example:

Due Date
01/04/2012
02/04/2012
03/04/2012
04/04/2012
05/04/2012

if i used between and operators:
select * from tbl_name where Due Date between '02/04/1987' and '04/04/2012'...
Here only i got this O/P:
03/04/2012
04/04/2012... but i want to get

02/04/1987
03/04/2012
04/04/2012... This only i need....Just tell the solution...

Thanks In Advanced