How to enable routing on a 2960 series?

Your 2960 need to run IOS Version 12.2.55 or higher to enable lanbase-routing
To enable routing we need two things. Firstly activate the functionality sdm prefer lanbase-routing and subsequently enable ip routing.

You need to reload for the change to take place.
After the system reload, you can use the show sdm prefer command to verify the change.

An example of routing between vlan.

Now if you ping from the vlan 1 to the vlan 2 it should work.