How to save text messages when getting a new iphone?

I cracked my iphone 5s screen (the phone still works) so badly that I have to send it in and get a new one in return.

When i'm feeling really upset I look back at old texts and they are really important to me.

I know that I can save my photos on a computer but is there anyway to keep the texts and import them on the new phone once I get it?

That would be a question for the techs at your phone store.

I think icloud is the way.
I haven't tried it, but I do remember hearing it from a youtube tech video saying they can backup the entire phone to icloud and restore it to whichever iphone device they own.

But since I haven't tried it, I can't guarantee you.