Alan

See below:

This should allow you to answer both your questions.

Set y = 0 and solve the resulting equation for t.  There will be two values; choose the only sensible one.

Thanks.  You're almost right!  I added the square root of 75 instead of subtracting it.  I've now edited and corrected.

Like so:

$\sqrt{12}-\sqrt{75}+\sqrt{147}=\sqrt{3*4}-\sqrt{3*25}+\sqrt{3*49}=(2-5+7)*\sqrt{3}=4\sqrt{3}$

Like this for Q1:

Now let's see you attempt something!

See https://web2.0calc.com/questions/the-fundamental-of-calc-pt1#r1, for the approach.

Split the integral into two integrals (note the upper limit on the first integral and the lower limit on the second integral):

$\int_{-1}^{2}f(x)dx=\int_{-1}^{1}(3-x^3)dx+\int_{1}^{2}x^2dx$

I assume you can do these individual integrals.

Yes.

Correct!

This should help:

I should have said the turning point values of t, not x!