iOS 7.1 and 7.1.1 cannot be jailbroken with Evasi0n7 at the moment, but there is another program that states it can semi tethered jailbreak your iOS 7.1 device. This is Geeksn0wjailbreak for iOS 7.1 Apple smartphone that supports only ONE cell phone, iPhone 4, some iPod touch models and iPads. In other works, if you have iPhone 5S, 5c, 5 and 4S you cannot use Geeksn0w jailbreak on them. You can follow this guide on how to jailbreak iOS 7.1 using GeekSn0w, recent tool from hackers. 
The program has been developed by Andrea Bentivegnaknown as @Blackgeektuto. He is not associated with the famous teams in the jailbreaking community, yet his tool is free to download and use. Don’t expect Geeksn0w iPhone 4 iOS 7.1 jailbreak development to work as other tools. You need to install JDK on your Mac or Windows PC before jailbreaking. The status you will get is semi tethered. There is no untethered solution for the two latest versions of iOS7 released yet. Most hackers are believed to be working on the next iOS8 jailbreak development and they have no time to release programs for current firmware versions.
There is not many iOS 7.1 jailbreak news at the moment. Still a lot of users wonder if Geeksn0w jailbreak for iOS 7.1 and 7.1.1 is real or not. We’ll assure you this is a real solution. As always, if you choose to jailbreak you will do this at your own risk since any jailbreaking voids Apple warranty.
At the moment this tool is updated to version 2.9. It is believed to be stable enough to be used by users. Once again, iOS 7.1 Geeksn0w jailbreak is available for iPhone 4 only [it also works for iPod touch and iPad devices]. Users who have used this tool in the past and got tethered status can download Geeksn0w 2.9 and transfer their tethered jailbreak to semi tethered.
The jailbreak is not a fake so you have nothing to worry about.