Calculate surface limited by curve

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How to calculate the surface limited by the curve described with the two equations:

$x = 3+cos(t)$

$y=4sin(t)$

The formula we use is the one shown below:

$\int_a^b |y(t).x'(t)| \,dt$

Now I'm wondering what I should use for $a$ and $b$. I also have no idea how to imagine a function like this so I don't know what surface is limited.

Thanks.