I would like some help to understand better a specific part of the proof. The goal of the proof is to prove the $u(t)$ definition.
By the definition of a generalized function: $$\int_{-\infty}^{\infty} f(t)u(t)dt = \int_{0}^{\infty} f(t)dt$$
Step 1: $$\int_{-\infty}^{\infty} f(t)u(t)dt = \int_{-\infty}^{0} f(t)u(t)dt+\int_{0}^{\infty} f(t)u(t)dt= \int_{0}^{\infty} f(t)dt $$
Step 2: $$\int_{-\infty}^{0} f(t)u(t)dt = \int_{0}^{\infty} f(t)[1-u(t)]dt$$
I do not understand the derivation of RHS of step 2. How?