Although we usually assume a uniform partition when performing numericalintegration, there are occasions where a non-uniform partition might be moreuseful. For example, consider the integral 01x2+12dx.Show the partition {0.00,0.21,0.44,0.69,0.96,1.00} gives Riemann sumswhere a calculator is not needed to find the values off(xk), except for thefinal value which is just the square root of2.Calculate the left and right Riemann sums and average them, which thus givesthe result of the trapezoidal rule with a non-uniform partition. If you wantedtodo a similar calculation which provided more accuracy, what new partitioncould you use? (Hint: consider the perfect squares which lie between 1000and 2000.)