Coach Flexible

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Can someone please tell me if I am understanding this correctly. I am looking at booking a flight and Coach Flexible is $2 more than Coach Non-Refundable. If I book Coach Flexible will I automatically be upgraded to First Class if upgrade seats are available?

I tried searching for the answer and this was what I understood from reading other posts.

Thanks
Be careful, a flexible coach fare isn't always upgradeable. It usually books into a T fare bucket or something. After you choose your flights, proceed to the next page where it summarizes your flights. Where it says cabin, it will have your fare class in parentheses after it. It needs to be a Y or B fare to be automatically upgraded. I think you specifically need to choose Preferred Upgrade from the fare classes to be given those fares...
Thank you. That is what I needed to know.