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    Part b)
    Where do I start?
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    My teacher has always told me to use this:

    Integral of Y(DX/DT) to work out the area but no idea how to get it into that format :/
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    Well, you know how to find the integral in respect to x, right?
    It's ∫f(x)dx from x=-1/2 to x=1

    So substitute f(x) and dx with equivalents in terms of t.

    f(x)=3t-2sin2t
    Now, you have f(x) in terms of t.

    But what's dx in terms of t?
    Hint: If dx/dt=x', then dx=(x')dt

    After that, you should get something similar to the answer (without the bounds). Replace the bounds of x with equivalents in terms of t, and you should get the bounds of t.

    Cheers!

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Updated: June 20, 2012
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