IF the upper limit and lower limit are the same, the limit will be equal to zero.
IF there is a constant, k, multiplied by the function f(x), you can move that to the front of the integral, multiplying k with the end result.
IF there are two integrals with the same function f(x) being added together with one having a top limit, b, and another one with a bottom limit, b, you can use the top limit and the bottom limit respectively of the two integrals. Now you have a more simple integral.
IF you need to find the integral with the opposite of the current upper and lower limit, you are able to switch the upper and lower values, but adding a negative to the integral is needed.
IF there are two different functions, f(x) and g(x), added/subtracted together, you can separate the two functions with the sign in between them in order to integrate them easier.