Geodesic
Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation
Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1335-1355

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In this article we obtain characteristic properties of piecewise-polynomial functions (“spline” functions) that have least deviation from zero in the metric of $C$. This has allowed us to obtain quadrature formulas with least estimate of the remainder on a number of classes of differentiable functions. 
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     author = {N. P. Korneichuk and N. E. Lushpai},
     title = {Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation},
     journal = {Izvestiya. Mathematics },
     pages = {1335--1355},
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     volume = {3},
     number = {6},
     year = {1969},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a10/}
}
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N. P. Korneichuk; N. E. Lushpai. Best quadrature formulas for classes of differentiable functions and piecewise-polynomial approximation. Izvestiya. Mathematics , Tome 3 (1969) no. 6, pp. 1335-1355. http://geodesic.mathdoc.fr/item/IM2_1969_3_6_a10/