this is probably a very common question, but i couldn't find the answer on my books.  

is every darboux function the derivative of a function? even the nowhere continuous ones?



antiderivative of a darboux function
No. Unfortunately, there is no such simple criterion for a derivative. At least none is known. 


Ref: Bruckner, Andrew, Differentiation of real functions. Second edition. CRM Monograph Series, 5. American Mathematical Society, Providence, RI, 1994. xii+195 pp. ISBN: 0-8218-6990-6, MR1274044 (94m:26001) 


