In this work, the concepts of quantum derivative and quantum integral are renamed to be the left quantum derivative and the left de…nite quantum integral. Symmetrically to the left, a new quantum derivative (the right) and de…nite quantum integral (the right) are de…ned. Some properties of these new concepts are investigated and as well as according todo these new concepts some inaccuracies in quantum integral inequalities are corrected. Moreover, some new quantum Hermite-Hadamard type inequalities are established.