how to upgrade oracle 10g R1 to oracle 11g R2
Please check the link below.
ORACLE-BASE - Upgrading to Oracle Database 11g
Also you can go for export/import using datapump to achieve upgrade.
Pl identify exact versions of 10gR1 and 11gR2. For direct upgrades (using DBUA or scripts), you need to be at 10.1.0.5 or higher - Preparing to Upgrade Oracle Database
The upgrade process is documented in the Upgrade Guide - Contents
Pl also review MOS Doc 419550.1