IPhone 5s not dinging when I get a new email?

So I got the iPhone about a week and a half ago, and I'm having an issue with my email. I have both of my accounts set up, exactly as they were on my iPhone 4. I had iOS7 on my 4 as well as clearly on my 5s. But when I get new emails it is not letting me know.

I do not want an actual notification, like a text message or something. I just want it to ding when I get new emails and for the little red circle with the number of new emails in it to appear. I have to physically open the email app in order for it to update, and by that time I have like 20-30 missed emails. These include my school emails, which are important.

I can't find anything to fix this issue through google. So any help on getting it to ding and show the number of new emails without me having to open the app would be great.

Go to Settings > Notification Center > Include. You find your settings here.