Find the values of $p,\ q,\ r\ (-1<p<q<r<1)$ such that for any polynomials with degree$\leq 2$, the following equation holds:

\[\int_{-1}^p f(x)\ dx-\int_p^q f(x)\ dx+\int_q^r f(x)\ dx-\int_r^1 f(x)\ dx=0.\]

[i]1995 Hitotsubashi University entrance exam/Law, Economics etc.[/i]