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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 = cf (x)dx |
f (x)dx +  f (x)dx =  f (x)dx |
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