A graph of the function \(y=f(x)\) is sketched on the axes below;

The value of \(\displaystyle\int_{-1}^1 f(x^2-1) \:dx\) equals (a) \(\dfrac{1}{4}\qquad\) (b) \(\dfrac{1}{3}\quad \quad\) (c) \(\dfrac{3}{5}\quad \quad\) (d) \(\dfrac{2}{3}\).

Can we write down an equation for \(f(x)\) for each distinct interval?

Can we then write down what \(f(x^2-1)\) is?

If the values of \(x\) run from \(-1\) to \(1\), what values does \(x^2 -1\) run through?