Excel 2000, 9.0

I'm trying to establish a condition in a SumIf formula stating a range of dates.

e.g. Column A: Date, Column B: Cost

If the date in Column A is between 2/1/05 and 2/28/05, add expense from Column B.

I can only get it to add "later than" by indicating
=SUMIF('Men''s'!A4:FA93,">1/31/04",'Men''s'!B4:B293)
But that just adds up Column B ofr the rest of the year...

Any help's appreciated!