Integral of an L_p function

Question

Let $p \ge 1$ and $f$ be a Lebesgue measurable function on $\mathbb R$ such that $\int_{\mathbb R} |f(x)|^pdx < \infty$. Show that, $$\int_{\mathbb R} |f(x)|^pdx =\int_0^{\infty} pt^{p-1}\lambda(\{x : |f(x)| > t\})dt$$ where $\lambda$ denotes the Lebesgue measure.