Yes, every field is an integral domain.
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The are under the curve on the domain (a,b) is equal to the integral of the function at b minus the integral of the function at a
The range depends on the domain. If the domain is the complex field, the range is also the whole of the complex field. If the domain is x = 0 then the range is 4.
Electric flux.
It is the integral (or sum) of the joint probability distribution function of the two events, integrated over the domain in which the condition is met.
The equation is Integral of p(x), where p(x) is the probability distribution function, and x ranges over its whole domain. For a discrete variable, the integral would be replaced by summation.