Approximating this integral with midpoints

[CookieSalesman]

I have an integral from 0 to 1, of sin(x²).
I need to, with n=5 rectangles midpoint approximate it.

I've figured that I need something like i=1 and ending at 5 (right?), and the equation is just sin(x²) Δx
Delta x is 1/5.

Are those the correct steps?
I think that all I need to do...
is... uhh... Well, actually I'm not sure how to change x². Should it be x_i²?

If that's true, then I think all I need to do, to midpoint approxy is keep on incrementing i, and I think it naturally gives me a midpoint, right?

 

[Mark44]

I have an integral from 0 to 1, of sin(x²).
I need to, with n=5 rectangles midpoint approximate it.

I've figured that I need something like i=1 and ending at 5 (right?), and the equation is just sin(x²) Δx
Delta x is 1/5.

Are those the correct steps?
I think that all I need to do...
is... uhh... Well, actually I'm not sure how to change x². Should it be x_i²?

If that's true, then I think all I need to do, to midpoint approxy is keep on incrementing i, and I think it naturally gives me a midpoint, right?

Yes, you need to have an x value (x_i) for each subinterval. If x_{i - 1} and x_i are then endpoints of a given subinterval you need to evaluate your function f at $\frac{x_{i - 1} + x_i}{2}$, the midpoint of that subinterval.