How do I automatically sum a variable number of rows between two delimiters?

I get a monthly spreadsheet from an accounting program and add formulas to
it to make it usable for others.

The sheet contains info about projects; each project is a set of a variable
number of rows. There is always a non-bold "F" at the start of the set and a
bold "F" at the end. The end of the set I want to sum is always in the same
position relative to where the sum function is, but I can't work out how to
find the other end, in a formula. This has to be formula driven as there are
too many sets to do it manually.

Example:
A B C
Job1 JobName F
Line1 500
Line2 1000
Line3 1500
Line(n) 1000
Job1 JobName F
(SUM FUNCTION)