COUNTIF function not counting dates on 31st

Hi I am using the formula:
=COUNTIF($J$12:$J$3081,">="&DATE($T$2,IN1,1))-COUNTIF($J$12:$J$3081,">="&DATE($T$2,IN1,31))
To count the number of times dates appearing in a certain month appear in the J column. However this is not picking up dates which are on the 31st, I've included >= so not sure why this is happening.

The way the formula works is that the first COUNTIF counts all dates on or after the 1st of the month (including dates beyond the end of the month)......the second COUNTIF then subtracts all those dates that are beyond the end of the month (so that the final result is only dates within the correct month), so you don't want >=, you want >.

....but obviously some months don't have 31 days so that won't work correctly in February, for instance, unless you change the 31 each time, better to use this version with the 1st of the next month (where you do still want >=), so that the same formula will work for any month

=COUNTIF($J$12:$J$3081,">="&DATE($T$2,IN1,1))-COUNTIF($J$12:$J$3081,">="&DATE($T$2,IN1+1,1))

or in Excel 2010 you can do that more simply with COUNTIFS, i.e.

=COUNTIFS($J$12:$J$3081,">="&DATE($T$2,IN1,1),$J$12:$J$3081,"<"&DATE($T$2,IN1+1,1))