Evaluate the limit by first recognizing the sum as a Riemann sum for a function defined on [0,1]

Question

lim_n→∞∑ⁿ_i=1(i⁴/n⁵+i/n²)

I got Δx=1/n and x_i=i/n but I'm not sure how else to proceed by the Riemann sum method.

Answer 1

i⁴ / n⁵ + i / n² = (i⁴ / n⁴ + i / n)(1/n) = [ (i / n)⁴ + (i / n)] (1/n) = f(x_i)Δx

The value of the limit is ∫ _{(0 to 1)} [x⁴ + x]dx.