Proof: Using properties of the integral

Question

Not sure where to start; can someone give me a hint?

Problem:

If $ f $ is Riemann integrable and if $ \lvert f(x) \rvert \le M $ on $[x,y]$ then $ \lvert \int^b_a f d\alpha \rvert \le M[\alpha(y)-\alpha(x)]$ .

Answer 1

Hint:

$$L(z) - L(b) = \int_b^z f\, dt$$