I'm sure there may be a better way to do it but one, quick and dirty way would be to use column D with a formula that tests each "C" cell to see if it falls between A1 and B1. If it does, have the formula print an "X" and then simply count the "X's".
D Column Formula: =if(and($c1>=$a$1,$c1<=$b$1),"X","") -- Put formula in cell D1 and drag through D100
Cell D101: =countif($c$1:C$100,"X")
A simpler way could also be to put a formula in cell C101: =subtotal(9,$c$1:$C$100) -- After you place the formula, you then apply a filterto cells C1:C100 testing for greater than/or equal to A1 and testing for less than/or equal to B1. Apply the filter with the C1 through C100 highlighted and view the "COUNT" in the status bar.
I hope this helps!