I have been using framaroot to root my androids and some of my friends androids. So far I have had no issues rooting a phone so yes by experience this is indeed accurate. I have rooted Samsung galaxy S2, S3, Lg Lucid, and a few others which I cannot remember. I have not tried rooting the galaxy S4 with frama so I am not sure if it works.
I discovered this app googling around and downloaded different versions of framaroot in case the app could not find an exploit on the android I'd try a higher version or lower version. So one of the following versions should work. I would start with framaroot1.3 and if that does not work try 1.4.2 and so on. Someone known by alephzain created framaroot and I think I heard something about him working for google or what ever, but thanks to him he made rooting a lot easier. Once framaroot successfully roots your phone you have to restart and it will automatically have superuser installed. Before rooting make sure your phone is charged above 70% and you enabled usb debugging. I also placed a root check pro.apk to check if your phone is rooted. Hope this works for you!
Extract the .rar file with winrar and place the folder inside your sdcard on your android or internal storage.
