Counting dates

[Bardee]

I have a date range, (example Jan. 13, 2014 to Feb.20, 2014) and am trying to find a formula to count the number of actual missed days during this period, based on another range of non-consecutive dates (example Jan 3, Jan15, Jan19, Feb3, Feb28). Answer would be 3.
Anyone have any suggestions?

[Kaper]

use countifs
something like

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E dates to be checked
F1 start date
F2 finish

make sure dates are real excel dates (not just texts which only look like a date)