If we for example set \( n=1 \), we obtain $$ \begin{equation*} P_1(x) = y_0\frac{x-x_1}{x_0-x_1}+y_1\frac{x-x_0}{x_1-x_0}=\frac{y_1-y_0}{x_1-x_0}x-\frac{y_1x_0+y_0x_1}{x_1-x_0}, \end{equation*} $$ which we recognize as the equation for a straight line.

The polynomial interpolatory quadrature of order \( n \) with equidistant quadrature points \( x_k=a+kh \) and step \( h=(b-a)/n \) is called the Newton-Cotes quadrature formula of order \( n \).