So I just have a question about Riemann Sums.

I give an example to explain my question.

Let's say I wanted to find the area under a curve of f(x)=x^2 on the closed interval [0,1]. The area would be equivalent to

lim (n-->inifnity) ((n(above)Sigma(i=0) (f(x(subi))*(deltax)))

Hopefully someone can understand that.

It should look something like this

So delta x would be (1-0)/n which is 1/n

But how do I find x(sub i) so I can plug it into f(xsubi)? Is there a universal formula that I may use with Riemann Sums to find x(subi) even for more complex problems?

Thanks