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.