I wish to add up Column B but only those rows (in the column), who's date in Column A is less than today, what formula would I use?

Eg. Col A has dates, Col B has values

25/03/13 - 862
26/03/13 - 1089
27/03/13 - 345
28/03/13 - 6727
29/03/13 - 782
30/03/13 - 827
31/03/13 - 28
01/04/13 - 373
02/04/13 - 87298

As today is 31/03/13, I would only add Col B up as far as 30/03/13