I'm having a hard time proving the following:
Let $f: [a, b] → \mathbb{R}$ be an integrable function. Show that $\lim_{\delta\to 0+}$ $\int_{a+\delta}^b f(x)dx = \int_a^b f(x)dx$
If the function was continuous, I would try using the mid value theorem for integrals. But I only know $f$ is integrable. Is there something I'm missing?