Area enclosed by line and curve - integration

[donjt81]

Hi guys,

I need some help on this. It is in the integral section so I am assuming you use integrals for this. Can someone point me in the right direction.

Find the total area enclosed by the line x = -3 and the curve x = 2y - y^2

 

[courtrigrad]

You have to take $$\int_{a}^{b} f(y) - g(y) \; dy$$ where $$f(x)$$ is the greater function. To get the limits of integration set $$- 3 = 2y-y^{2}$$

 

[donjt81]

so let me see if I understand this correctly.
$$\int_{-1}^{3} (2y-y^{2}) - (-3) \; dy$$

is that correct?