Count Days between Two Dates within Specific Dates

[LoganCoffin]

I'm not sure if the title makes much sense, but where is what I've been trying to lookup documentation or help for. 

I have two columns with dates, [Start Date] and [End Date] for Leave of Absences.
I need to count the number of days within the 1st of the Month to the 16th. 

For example:
If the [Start Date] is January 28th and the [End Date] is February 5th, the total days would be equal to 5.
If the [Start Date] was February 8th and the [End Date] was February 14th, the total days would be equal to 7.

If anyone could help, or point me in the right direction I'd appreciate it.