Using COUNTIF to return the sum of dates that fall within a Month/Year range.

I want to use a COUNTIF to return the sum of all the dates that fall within a given month/year.

For example:
E1 Contains the date July-2009

Column A has date entries such as July 3, 2009, July 18, 2009, August 4 2009...

In F1 I want to return the sum of all dates that fall within the month of E1.

I attached an example, I appreciate any help with this.

thanks,
Nick