Tracking time spent in iOS applications

I know RescueTime exists for Android but I do not see anything like it for iOS. I'm guessing such an app may not be possible on iOS because of the permissions and how apps have been sandboxed from one another. However, I'm hoping that I'm wrong.

Has anyone found an app which at the end of the day a user could look and see a list which shows the total active time spent in different applications for that day?

I'm looking for something like the following:

Summary for YYYY-MM-DD
Total Time: 2h28m

 - Safari: 48m 
 - Tweetbot: 32m 
 - Mail: 23m 
 - Cooks Illustrated: 22m 
 - Yelp: 12m
 - Messages: 8m 
 - OmniFocus: 3m

There is no such app for iOS because of its security limitations, you can see such statistics only once jailbroken.

That being said, you will find something close to what you are looking for but only if you are using iOS 9. Do the following: Settings > Battery and under Battery if you scroll down by a little bit, you will see battery usage for the last 24 hours or for the last 7 days in % and in min/h on screen time and background usage also in min/h, something like the image below.

The beta of iOS 12 includes Screen Time which solves this problem rather conclusively at the OS level. Here's a couple of my screenshots from revent use: