How to Find the Area Bounded by a Curve Using Integrals

[SherlockOhms]

Find the area bound by the curve y = x^3 - 2x^2 - 5x + 6, the x-axis and the lines x = -1 and x = 2. The answer is 157/12.

The curve cuts the x-axis at x = -2, 1 and 3. I've shown my general idea on the attachment. I didn't end up with the correct answer so could somebody explain to me where I've gone wrong?

 

[SherlockOhms]

 

[Mark44]

Find the area bound by the curve y = x^3 - 2x^2 - 5x + 6, the x-axis and the lines x = -1 and x = 2. The answer is 157/12.

The curve cuts the x-axis at x = -2, 1 and 3. I've shown my general idea on the attachment. I didn't end up with the correct answer so could somebody explain to me where I've gone wrong?

Your integral for the interval [1, 2] is not set up correctly. It should look like this:
$$\int_1^2 (0 - y)dx $$
Do you see why?

BTW, do not discard the three parts of the homework template. They are there for a reason.

 

[SherlockOhms]

Your integral for the interval [1, 2] is not set up correctly. It should look like this:
$$\int_1^2 (0 - y)dx $$
Do you see why?

BTW, do not discard the three parts of the homework template. They are there for a reason.

Thanks for that. The graph goes below the x-axis.
I sent that from my phone and the templates don't actually show for you to use.
Thanks again.