I think the actual "Integrity Field" Module is broken. 

Integrity Field

"incrase the Armor Strength of all ships in fleet"

Assumption: Its supposed to give more armor rating and not more Htpoints (which it correctly doesn't do)

I ran the following test : 

1. Use a Support Hull and attach (1x per ship) the following Modules to it: 

- Field generator  (+ Shield Strength)

- Missile Disruptor ( + Missile Defence)

- Integrity Field (+ ???)

2. Build 8 Ships of this model

3. Write down the numbers of "Shield Strength (S)", "Missile Defence (MD)" and "Armor Rating (AR)"

1.  1 Ship  -> 5 (S), 2 (MD), 0 (AR)
2. 2 Ships -> 20 (S), 8 (MD), 0 (AR)
3. 3 Ships -> 45 (S), 18 (MD), 0 (AR)
4. 4 Ships -> 80 (S), 32 (MD), 0 (AR)
5. 5 Ships -> 125 (S), 50 (MD), 0 (AR)
6. 6 Ships -> 180 (S), 72 (MD), 0 (AR)
7. 7 Ships -> 245 (S), 98 (MD), 0 (AR)
8. 8 ships -> 320 (S), 128 (MD), 0 (AR)

So my guess is that this module is "broken" aka not working as intended. 

Edit:

I have not tested the advanced  Module called  "Hull Enhancement Field" as i am playing a game with no Asteroids.

Edit2:

The tooltip calls the increase "Armor Strength", while the Tooltip when hovering over the "Armor Symbol" on Ships/Fleets/Designer calls it "Armor Rating"

On the Shield side of things, they are both called "Shield Strength", so i assume this miss-match in wording is an oversight ? 

kind regards, 

Q-Wulf

ps.: is there a bug tracker one can add to ?