I've been able to solve parts A, B, and D of this question. But I'm really stuck on Part C. Could someone offer some insight?

Part A:

This follows from integration by parts:

$\displaystyle u = f(x)$, $\displaystyle v=x$

$\displaystyle du =$ $\displaystyle f'(x)$, $\displaystyle dv = dx$

Part B:

Substitute $\displaystyle y=f(x)$, $\displaystyle dy = f'(x)$. It follows that x=g(y). Then we substitute values into formula from part A, remembering to change the bounds: When x=a, y = f(a). When x=b, y = f(b).

Part c:

Stuck on this.

Part d:

Using formula from Part B, we simply plug in values and find that the integral evaluates to 1.

Thanks,