Expressing the limit?

Question

lim n-> inf ∑ Bot(i=1) top (n) [4/3(xi*)^2+6(xi*)^5] ∆x, [0,2]

how do you work this

Answer 1

The limiting value is clearly the integral

⌠[(4/3)x² +6x^5] dx evaluated from x=0 to x=2

and that is (4/9)x^3 + x^6 = (4/9)(8) + 64 - (0+0)

64 + 32/9 = 608/9