Fraps.com is a good site altogether. It's pretty safe for children and is 100% safe. It offers information on their product and is Fraps' official site. All in all, I saw nothing wrong with this website. Very trustworthy.
In terms of the software and what I was able to gather, it seems to be pretty legitimate. No scams, no viruses, it's pretty safe to download. 100% legitimate.
It's good if you pay for it. The free version only limits your recording to 30 seconds. If you want to upload your recorded videos to YouTube, then it is best to pay for it. If you just want to review your memories that you had when playing your game, then the free version is enough.
There are some problems with it. First, A recorded video (that was under 30 seconds) may take about 5 minutes to be downloaded (at a constant rate of 600 k/s). That's because Fraps has very good quality. If you don't care what the quality is, then I recommend Bandicam. The free version is enough for any video.