Two inequalities for the integrated modulus of continuity have been investigated for periodic continuous real-valued functions f with seminorms P. Let E_n(f) is the best approximation of n order of the function f. It has been proved that the inequality E_n(f)≤K∫₀^Π/(n+1)ω₁(f′, t)dt is correct with the constant K=0.2961887, where ω₁ is the continuity modulus of the first order for the function f with the step t relatively the seminorm P. Estimation of the periodic function seminorm by the second integrated modulus of continuity has been established with the smaller constant.