I want to use 2 different Public IP in same Ubuntu 14.04 Server. I am using 2 Different routers with IP forwarding.
I have 2 ethernet ports eth0 and eth1. In my scenario Only one Static ip at a time is working. How can I make both public IP working remotely? Both IP are from different ISP.
What could be the possible solution and ethernet script.

Depends on what you are doing. There is nothing wrong with what you have.

If you are connecting to a 192.168.10.xx address it will go out eth0.
If you are connecting to a 192.168.4.xx address OR an unknown address it will go out eth1.

You can only have ONE default gateway, and that default gateway is designated to be 192.168.4.1 - so any unknown outgoing addresses will be sent to that address via eth1.

You CAN specifiy specific addresses to use a different route - but these are something you do manually/put in a script to set at boot time. You would have to look at setting static routes - for Ubuntu I believe this file is /etc/network/interfaces