Finding integration limit which produces a prescribed value for a definite integral

Consider a function, f(x) which is the definite integral of g(s) from s=constant to s=x. I am looking for an efficient way to determine the value of x which produces a specific value, b, for f(x).

That is, determine x such that f(x)=b.

I would like to have x determined with a high degree of precision.

Answer 1

[Walter Roberson]

basically you either do a zero search for f(x)-b, or you minimize (f(x)-b)^2