Sure...

=SUMIFS(B:B,A:A,">="&W2,A:A,"<="&EOMONTH(W2,0))

We want to sum values in column B that fall within specific date boundaries in column A.

B:B is the sum range

A:A are the dates

">="&W2 is the lower date boundary.

W2 contains the date 4/1/2013. So the lower date boundary is dates greater than or equal to 4/1/2013.

"<="&EOMONTH(W2,0) is the upper date boundary.

The EOMONTH function returns the End Of Month date that is n months from the referenced date. The referenced date is 4/1/2013 in cell W2. n months = 0 in this case so EOMONTH returns the end of month date for Apr 2013 which is 4/30/2013.

So, sum the values in column B that correspond to dates in column A that are greater than or equal to 4/1/2013 AND are less than or equal to 4/30/2013.

=SUMIFS(B:B,A:A,">="&W2,A:A,"<="&EOMONTH(W2,0))