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Can the result of a definite integral be negative?

If I am integrating a definite integral, sometimes it is possible to end up with a negative value - but I thought a definite integral was an area, so what happens if my result is negative?
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the area below the X axis is counted as negative.  Also you have probably integrated from say 1 to 3 where 1 is at the bottom and 3 is at the top, well if you switch 1 to the top and 3 to the bottom, the integral comes out as -1 x the first integral.
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