In this paper, a new method to obtain the integration matrices using monic Chebyshev expansion is introduced. This monic Chebyshev integration scheme are used to approximate the integration included in integral problems. This approach generates approximations to the lower order derivatives of the function through successive integrations of the monic Chebyshev polynomials to the highest order derivatives. Then, the approximated problem for integral and integro-differential equations leads to algebraic systems. Numerical examples are given to demonstrate the proposed idea and robustness of the method.