Use the given form of the definition to evaluate the integral. int_0^3 (4-x^2)dx

Hello, I am trying to figure this out.

If f is integrable on [a, b], the following equation is correct.
int_a^b f(x)dx = lim_(n->infinity) sum_(i=1)^n f(x_i) Deltax text(, where ) Deltax = (b-a)/n text( and ) x_i = a + i Deltax.
Use the given form of the definition to evaluate the integral.
int_0^3 (4-x^2)dx

First thing's first, just plug absolutely everything in:
b = 3, a = 0, Δx = (3 - 0)/n = 3/n
f(x_i) = f(a + iΔx) = f(0 + (3i/n)) = 4 - (3i/n)²

f(x_i)Δx = (4 - (9i²/n²))(3/n) = (12/n) - (27i²/n³)

Now use the rules of summation to split everything up
∑{i=1,n} (12/n) - ∑{i = 1,n} (27i²/n³)
(12/n) ∑{i=1,n} 1 - (27/n³) ∑{i=1,n} i²
(12/n)(n) - (27/n³)(n(n+1)(2n+1)/6)

Now just simplify all that mess and evaluate the limit as n->∞ (it will converge). Check your answer by evaluating the integral via the power rule.