Find the area between y = -x^3 + 5x^2 - 6x and the x-axis

Why are you struggling with this. It is just an integration problem. Are you possibly wondering why you get a negative value? Don't get a negative value. We're looking for an area. That's always positive.

Do it in two pieces. [0,2] and [2,3]

Let's see what you get.
 
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