Cauchy's Formula for Repeated Integration

Repeated integrations can come up pretty often. It's a bit of a pain but the OG has formula for this. Proof is via induction.

$$_n\int_{a}^{t} f(x) d x^{n}=\frac{1}{(n-1) !} \int_{a}^{t}(t-x)^{n-1} f(x) d x$$