Integrals on [0, +inf] as limits

Stream: Is there code for X?

[Anatole Dedecker]

I don't know measure theory in depth so this might be a stupid question, but is there a way I could prove $\int_{\mathbb{R}_+} f\ d\mu = I$ if I already know $\int_0^x f\ d\mu \xrightarrow[x\to+\infty]{} I$ ?