Please answer question in python on sagemathcloud

Answer the following questions to the best of your ability. Solutions should be typed. Any plots or graphs should be included with the question (please include the questions in your solutions). Newton and Lagrange Interpolating Polynomials Consider fitting a polynomial to the following set of points. {(-2, -4), (3, 1), (6, -2), (8, 5)} Write code that fits this data set with a 3^rd order polynomial using a Newton Interpolating polynomial call this P(x). Now use Lagrange Interpolation to fit the same data set with a polynomial. Plot the results of your work (points, and function). Using a quadrature rule exactly evaluate: integral_-2^8 P(x) dx Answer the following questions to the best of your ability. Solutions should be typed. Any plots or graphs should be included with the question (please include the questions in your solutions). Newton and Lagrange Interpolating Polynomials Consider fitting a polynomial to the following set of points. {(-2, -4), (3, 1), (6, -2), (8, 5)} Write code that fits this data set with a 3^rd order polynomial using a Newton Interpolating polynomial call this P(x). Now use Lagrange Interpolation to fit the same data set with a polynomial. Plot the results of your work (points, and function). Using a quadrature rule exactly evaluate: integral_-2^8 P(x) dx