My math books, in the introductory chapter of indefinite integrals (they call them primitives, and a primitive of a function is any function who's derivative is the original function) concludes the following thing: Any continuous function on the reals admits primitives on it's domain (that means that there exist indefinite integrals).
However I can easily come up with a counter-example. The function $f(x) = x^x$ is continuous on $[0,1]$ however there exists no such function $F(x)$ such that $F'(x) = x^x$.
Did I misinterpret the conclusion?