Change of integration range

Question

i found the following equation in "Fractional differential equations", written by Igor Podlubny on page 67.

For the interval [a,b] and $\tau$, $\xi$, t $\in(a,b)$, as well as $f$ continuous and $q,p\in \mathbb{R}_+$ the equation $$\int_a^t(t-\tau)^{q-1}d\tau \int_a^\tau(\tau-\xi)^{p-1}f(\xi)d\xi=\int_a^tf(\xi)d\xi\int_\xi^t(t-\tau)^{q-1}(\tau-\xi)^{p-1}d\tau$$ is valid.

My first idea was to substitute the integrand, but the only thing which is changing are the integration borders.

Now i wonder, why does it work?

Thanks, Matthias

Answer 1

The first part of the equation depends on tau but the second part is independent of tau, so equality can't hold?