Correct me if I'm wrong, but in your integral, your lower limit was minus infinity, right? But this curve has a bounded range from 0-100. I don't have the time to do the math, but won't that change your results?

ETA: I still don't have time to do the math, but this would definitely change your results. Try doing your calculation with the actual scale of 1-100 with mean at 50. You obviously won't be able to since we don't know what the SD is, but here we would have a definite lower limit, which would give you the actual answer. Your calculation doesn't hold when there's a defined lower limit.