Date range search

I am on my 3rd week searching and reading but could not find the answer to my query or I may have been using the wrong set of search keyword. To make the story short I need our member’s brilliant inputs on how to search my DATE SERIES [E2 – E6] if its inside the Date Range [B2 – C6]. If TRUE, cell [F2 – F6] will have the number of the date series
CELL [F2] shall contain NUMBER [4]
CELL [F3] shall contain NUMBER [3]
CELL [F4] shall contain NUMBER [1]
CELL [F5] shall contain NUMBER [0]
CELL [F6] shall contain NUMBER [0]

As far as I can see none of the values in col G are between values in B and C??