How to upgrade my iphone 3gs 4.2.1 firmware 06.15.00 jail broken to ios 5 or 6?

I have an apple iphone 3gs with ios 4.2.1 firmware 06.15.00
i need to upgrade it to ios 5 or 6 because i'm facing problem in installing application
so please say me how to do it by step wise

1. Backup your phone on iTunes.
2. Update your iOS from iTunes (I believe if you plug your device in you have the option of installing the most recent iOS).
3. Download evasi0n ( http://evasi0n.com/ ).
4. Run the application.
5. Your iOS device should already be plugged in. Just click Jailbreak.
6.It will ask you to unlock your device and tap on the jailbreak icon.
7. Wait a few more seconds, and then click the exit button.
8. You're all set! Use your backup to get all your apps and whatnot back.

1st you have to download IPSW file manually then upgrade via iTunes (Shift+upgrade) Key on your computer, Full safe guide in given bellow

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