[Gman1234]

Part b)
Where do I start?

[Gman1234]

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 :/

[aznkid66]

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!