(Solved): Program must, Calculate the integral of a function with Rectangle (10 Points), Midpoint (10 Points) ...

Program must, Calculate the integral of a function with Rectangle (10 Points), Midpoint (10 Points), Trapezoid (10 Points), and Simpson's (10 Points) methods. I. Calculate the \( f(x)=x^{3}+x^{2}+x-2 \) values for the \( x \) values between \( -4 \) and 4 (with \( 0.01 \) step (10 Points) II. Create an array with the calculated function values, such as Amay \( (1000,2) \). For each elen Array \( (i, 1) \) and Array \( (i, 2) \) correspond to the \( x \) and \( f(x) \) values. (10 Points) III. Calculate the integral of the function values stored in the array. (You must use Function properties for full grades)