Accidentally deleted the photos app icon from my iPhone 4s.

Question

I've read the previous threads on this topic but none quite fit the bill. I need to re-install the Photos icon, which has disappeared.
This happened while I was holding my phone but not paying attention; when I looked again the icons were all shaking. I don't know how the icon disappeared because the factory defaults don't offer a delete option, but the icon definately disappeared at that time.
The app itself is still there and, because it was running when I deleted the icon, I can currently still access it by double clicking the main button, where app (and icon) is still accessible there at the bottom of the screen. But this is not convenient for general usage, and if I hard close the app from there then I will have no way to open the Photos app.
I can't re-download the app because it is a factory default app and not available anywhere (and as such shouldnt be deletable!).
The icon isnt hiding anywhere amongst my subfolders, and I've checked for restrictions but there arent any.
Restetting the home screen layout to factory defaults presumably means I  will lose all the other app icons I have, and their sub folders etc,  which I dont want to do either.
I have now backed up my phone and all my photos etc, but if I restore my phone from a previous backup, I will lose the data and messages I've acquired isince then.
All I want to do is re-install the icon and make sure it links to the photos app that is still installed - surley that can't be so hard?
All help appreciated.
I don't have a Mac and run Windows 7 on a Sony VAIO. All versions of iTunes and IoS are up to date.
Patrick

Answer 1

PROBLEM SOLVED
ANSWER The exact same thing happened to me today.  I accidently deleted my Photo app (with over a 1000 photos in it) but I could still access it by pressing the home button twice.  This is because it was with the background running apps (when you press the home button twice it shows all the apps running in the background) but it would not let me drag it to the Home screen. 
Well so I was anxiously reading this thread at church to see what to do (I did a search for, 'I accidently deleted my Photo app' and how I came across this thread).  Anyway, I searched all my subfolders and everywhere IT WAS NOT IN ANOTHER FOLDER AND THE PHOTO ICON WAS COMPLETELY GONE FROM ANY OF THE DESKTOPS. 
Anyway, my phone was dying and no way to charge it so it died at church and so I connected it to my car charger in my car when leaving church and after the iphone came on again, there was the Photo App on my desktop! 
So my advice is to let it completely run out of it's charge then later plug into a charger.  I have the iPhone 4S going on almost 2yrs now and this is the first time this has happened to me!   I was in a hurry getting ready for church and pressed it accidently so I know exactly when it happened (when all the apps have x's and you can delete them ...). 
I always delete the backgound running apps to save battery power but I thought now I can never delete the Photo background running app or will lose everything!  Hope this works for you all.  I know I can connect it to my desktop and all but try this first - much easier...
Maria