TITLE: Continuous functions question
QUESTION [5 upvotes]: I am stuck on the problem:

Find all continuous functions $h$ satisfying 
  $$\int_{0}^{x}h(y)dy=\left [ h(x) \right ]^{2}+C$$
  for some constant $C$.

REPLY [2 votes]: HINT: The left hand side is known to be differentiable by the fundamental theorem of calculus, so the right hand side is also differentiable. Differentiate both sides to form a differential equation, and then solve that.