Step Function Proofs

Question

My notes give a lemma but I,m snuggling how the lemma actually works. Any help would be appreciated

Answer 1

From $0 \le f(x) \le \frac{\lambda}{b-a}$ it follows that

$$0 = \int_a^b 0 dx \le \int_a^b f(x) dx \le \int_a^b\frac{\lambda}{b-a}= \lambda .$$