Improper Integrals:
Integrals with “infinity” as a limit OR the range of integration produce an impossible value like dividing by 0.
Ex.

How to evaluate Improper unbounded Integrals:
Basically, make the infinity part into a variable “R” and then take the limit of that after you find the antiderivative.
This will then give you a fraction usually where the term with “R” turns to 0, and then you can find the area.

Special Rules for improper integrals:

Improper Bounded Integrals on [a, b]:
Introduce R again, as the limit, where the integrand becomes weird.
And then you take the limit of R from either “b-” or “a+”, aka from the left and the right

Complex Integrals:
Simply treat “i” as a constant, so it isn’t changed or anything.
It works with Riemann Sums, U-Substitution, Integration by Parts, etc.
However, there can be no absolute values, which means that: