LetI(f)?L(f)=? k=0 r ? ?=0 vk?1 a k? f (?)(X k ) be a quadrature formula, and let {S n (f)} n=1 ? be successive approximations of the definite integralI(f)=? 0 1 f(x)dx obtained by the composition ofL, i.e.,S n(f)=L(? n ), where $$\varphi _n (x) = \frac{1}{n}\sum\nolimits_{k = 0}^{n - 1} {f\left( {\frac{{k + x}}{n}} \right)} $$ . We prove sufficient conditions for monotonicity of the sequence {S n (f)} n=1 ? . As particular cases the monotonicity of well-known Newton-Cotes and Gauss quadratures is shown. Finally, a recovery theorem based on the monotonicity results is presented