Finding the area under the curve?

you start with a partition of [ 2 , 4]...most use a " regular " partition ...width 2 / n...then you note that x_i = 2 + i (2/n) , i =0,1,2,...n...;most now use a right hand Riemann sum...Σ { i = 1,2,3..n } f(x_i) (δ x_i) = Σ [ 64 - (x_i)³ ] ( 2 / n )......

(x_i)³ = [ 2 + i(2/n) ] ³ = 8 + 12 i(2/n) + 6 i² (2/n)² + i³ (2/n)³.......now you need to know sums of i , i² , i³ ...[Gauss formulas ]....finally you take the limits...that is the procedure..good luck....hopefully you get [ 68 ]