How to use Arrays in Functions like LARGE / Conditional Range

Please take a look at the spreadsheet.

1. I have two arrays (array formula 1 & 2).
And a large function which references the two arrays.
=LARGE(I4:I5, 2)

It does not work at all.
What should I do?

2. I want to calculate the sum of each section.
The name "Check" or "Verify" acts like a separator to draw the border of each section (see the spreadsheet).
Number of entries inside each section are not constant!

xxx }
xxx }
xxx }-- Add all numbers
Check ]
xxx ]
xxx ]
xxx ]
xxx ]-- Add all numbers
Verify }
xxx }
xxx }-- Add all numbers

The actual data is very long, so I need a way to define the range of each section by functions.
What should I do?