How can I convert the Riemann Sum into an Integral?

[ayae]

If I have a function c(x,Δx) that gives the area between x and x + Δx of a function.
The area under the function can be given by:
Sum from j = 0 to n-1 of c(b/n j,c/b)
As n tends to infinity and b is the upper limit of integration.

How can I convert this from a sum into a integral? I'm not sure if this is already in the form of a Riemann integral or not.

Thankyou in advance

 

[mathman]

c(b/n j,c/b)

Please clarify this expression.

 

[ayae]

Well c(x, Δx) is
1/2 Csc(x) Csc(x + Δx) s(x) s(x + Δx) Sin(Δx)
(Formula for the area of a triangle where Csc(x) s(x) are the length sides.

Where s(x) is the solution for z of f(z) == z Cot(x).

Where f(z) is the function I want to integrate. (I don't want to just integrate it f(z) dz)