Estimates of the error of interval quadrature formulas on some classes of differentiable functions

The exact value of error of interval quadrature formulas $$\int_0^{2\pi}f(t)dt -\frac{\pi}{nh}\sum_{k=0}^{n-1}\int_{-h}^hf(t+\frac {2k\pi}{n})dt = R_n(f;\vec{c_0};\vec{x_0};h)$$ obtained for the classes $$$W^rH^{\omega} (r=1,2,...)$$$ of differentiable periodic functions for which the modulus of continuity of the  $$$r -$$$th derivative is majorized by the given modulus of continuity $$$\omega(t)$$$. This interval quadrature formula coincides with the rectangles formula for the Steklov functions $$$f_h(t)$$$ and is optimal for some important classes of functions.