How do I export browsing history from iOS Safari?

I should be able to export my browsing history from ios version of Safari (and also Chrome, and other browsers), just like I can on an OSX or Windows machine.

Most ideally, I would like to export these histories into a file that I can then email or save somewhere. I do a lot of research and would like to keep that documented. I just shattered my screen glass and would like to do this before going to so-called Geniuses. I've already synced things like photos, to my MacBook Air.