Formula: Select A Range Of Dates Within A Range Of Dates?

In column B is a list of dates, which are broken out by fiscal year (FY=7/1/ to 6/30). Column C is a list of dollar amounts. Cell F3 is the query ‘start date’
Cell F4 is today's date, which will be the formula: =today()

Using a date range of F3:F4, I'm trying to get each cell bordered in red to query the dates in column B for each FY; then display the matching sum from column C.

For illustrative purposes I went and manually determined what the values should be displaying as of 7/22. Here are a couple of examples of how I am trying to get the formula to work.

Example 1
FY’08:
Start date- 7/1
End date- 7/22
Searching cells B1:B94, cells B1:B13 fall within the start and end date parameters listed above. Sum of cells C1:C13 is $45,112.00, which should display in cell F6.

Example 2
FY’09:
Start date- 7/1
End date- 12/13
Searching cells B95:B222, cells B95:B149 fall within the start and end date parameters listed above. Sum of cells C95:C149 is $150,873.03, which F7 should display in cell F7. How to I type up this formula; its way more challenging that I first thought!