Check if current date is between two dates Oracle SQL

You don’t need to apply to_date() to sysdate. It is already there:

select 1
from dual 
WHERE sysdate BETWEEN TO_DATE('28/02/2014', 'DD/MM/YYYY') AND TO_DATE('20/06/2014', 'DD/MM/YYYY');

If you are concerned about the time component on the date, then use trunc():

select 1
from dual 
WHERE trunc(sysdate) BETWEEN TO_DATE('28/02/2014', 'DD/MM/YYYY') AND
                             TO_DATE('20/06/2014', 'DD/MM/YYYY');