We now list several properties of definite integrals; though the proofs are not difficult, we will not give them here. They can be verified intuitively by considering the relevant areas.
|f (x)dx + g(x)dx = f (x) + g(x) dx|
|cf (x)dx = c f (x)dx|
|f (x)dx + f (x)dx = f (x)dx|