Analysis

[swift minnow]

I am not sure how to go about this question, can someone please help me?

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[karmic dust]

Basically, lower sum is a Riemann sum where you take the smallest value on each interval. Note that if the function is increasing, lower sum is the same thing as the left sum.

[swift minnow]

the left sum, so thats the one for -2 to 0?

[karmic dust]

What? No.
The left Riemann sum is when you take the value of the function at each interval on the left side on the interval.
So, the terms of the left sum are f(x(k))(x(k + 1) - x(k)), while the terms of the right sum are f(x(k + 1))(x(k + 1) - x(k)).

Note, by the way, that f(x) = x^3 is an odd function, and your partition is equidistant. So, the sum can be greatly simplified.

[swift minnow]

oh i see

i was thinking to do (-2)^3

[karmic dust]

That's just f(-2).

I recommend writing the general expression of the sum first.

[swift minnow]

this?

[karmic dust]

That is for the right sum, I'm pretty sure.

The left sum should be from k = 0 to n - 1.