Bounds for the perturbed Cˇ ebyšev functionals C (f, g) − μC (e, g) and
C (f, g) − μC (e, g) − �C (f, e) when μ, � 2 R and e is the identity function
on the interval [a, b] , are given. Applications for some Grüss’ type inequalities
are also provided.