Proving that a function is Riemann-stieltjes integrable

Let $ g$ a increasing function, and $ f$ integrable with respect to $ g$ in $ J=[a,b]$ proof that $ |f|$ is integrable with respect to $ g$

By definition if $ f$ is integrable with respect to $ g$ , for every partition $ P$ of $ J$ and for every $ \epsilon>0$ exists $ I$ in $ R$ such that if $ Q$ refine $ P$ then $ |S(Q,f,g)-I|< \epsilon $ $ |S(Q,f,g)-I|= \sum^{n}_{j=0}f(\lambda_{j})(g(x_{j}-x_{j-1}) $ then

$ \sum^{n}_{j=0}|f(\lambda_{j})|(g(x_{j}-x_{j-1}) \geq \sum^{n}_{j=0}f(\lambda_{j})(g(x_{j}-x_{j-1}) $

but i don’t know how to do

$ \epsilon \geq \sum^{n}_{j=0}|f(\lambda_{j})|(g(x_{j}-x_{j-1}) $

somebody can help me, please?