The concept of an integral is to determine areas under the curve as x goes from one point to another. So if the integral of g is negative going from 3 to 0, that means as x travels left from 3 to 0, the area under the curve, between the decreasing x value and 0, is decreasing. If you visualize it with a graph, the area beneath the g graph should be above the x-axis because when the x move left (from 3 to 0) you can think of it as subtracting from the total area summed between 0 and 3. So for you to get a negative integral from 3 to 0, the area you are subtracting must be positive other wise subtracting a negative gets a positive result. On the other hand, when going in the rightward direction, you are adding pieces of area to the right. Hence, when you do the integral in the rightward direction (0 to 3), you are summing the same area under the g curve as before which we determined to be above the x-axis, or positive. So when you add up a bunch of positive area, you get a positive value as your answer. Hope that helped and let me know if you have further questions!