The sine integral is defined as \(\operatorname{Si}(x)=\int_{0}^{x} \frac{\sin u}{u} d u\). Evaluate the quantity \(\operatorname{Si}(1)\) (that is, for \(x=1\) ) using a Gaussian integration formula to four significant digits using the zeros of the Legendre polynomial \(P_{2}(x)\). Using the actual value from a mathematical handbook (for example, Spiegel, 1973), estimate the relative and absolute error for the estimate.