Maths Question URGENT

Hi guys,
I am slightly confused by this question as I'm not sure why you would need to subtract the integral from the area of the rectangle. Since the area is negative, I thought the answer would be +24. Could you please clarify?

The 24 is the area between the curve and the x-axis (positive).
So to get R, subtract 24 from the area of bounding rectangle (60).

I'm not sure I understand. Why isn't the area between the curve and the x-axis, the area of region R?

Draw vertical lines up, starting from the x-axis and finishing at the curve. That region is what youre finding the area of when you perform integration. R lies on the other side of the curve.

Thank you! So could you please explain what this represents because I thought integrating was the area underneath the graph but clearly this is above the graph and below the x-axis?

Integration is the signed area between the x-axis and the curve. In this posted example the vertical lines start at the x-axis and go down so the function values and hence the signed area is negative.

Talking about the area under the graph is loose, and not correct in this case.