This is my assignment for analysis. When I tried looking more into this theorem, nothing online seems to state this test in a similar way. I don't really understand what the proof is telling me, so I am having a hard time proving it to be true.

Let g:[a, ∞ ) ->R be a nonnegative function satisfying g is Riemann integrable on [a,c] for every c>a and the integral from a to ∞ g(x) dx <∞ . If f: [a, ∞ ) statisfies

a) f is Riemann integrable for every c>a and

b) |f(x)|<= g(x) for all x in [a, ∞ )

then the improper integral of f on [a, ∞ ) converges and |integral from a to ∞ f(x)|<= the integral from a to ∞ g(x)

Any help explaining this theorem or starting this proof would be much appreciated.