How can the blockchain technology help boost the countries integrity level?

Good question, i think blockchain technology would be great for voting. 

Right now votes from elections are mostly counted with hand or sometimes electronically (in the western world). But you could use a blockchain to automate the process and also have more integrity because it would make it almost impossible to cheat. While if votes are counted by hand it's easier to commit fraud.

No more cheating in elections!

But the thing is, dictators or corrupt governments don't want this they rather keep ruling. So for them this would not be a good thing but it is for the people that are living in those type of places.