Reverse proxy : preserving base url

Hi.

I'm struggling since about 2days to create a reverse proxy with nginx.
Here is my situation :
I've a sub domain which we will call : sub.example.com
I've an internal application at 127.0.0.1:9090/app

What I would like :
I would like to proxy sub.example.com to 127.0.0.1:9090/app and i want to keep my URL as sub.example.com
So far I've done countless try without success.

The optimal situation would be that when I do :
http://sub.example.com/ I get the content from http://127.0.0.1:9090/app but without any change in the sub domain URL.

So for example if the internal app has http://127.0.0.1:9090/app/magical.css, my sub domain should be http://sub.example.com/magical.css (without app/)

Thanks in advance to anyone that is willing to help me.