Let $f$ be a Lebesgue integrable function on $[0,1]$ and $\int f = 1,$ and let $$g(x) = \int_x ^1 \frac{f(t)}{t} \text dt \quad x \in [0,1].$$ Calculate the integral of $g$.
I feel like I'm supposed to use Fubini's Theorem in this question but I'm a bit confused about the setup. Also since the problem should work for any $f$ I took a very simple function and calculated it to be $1$ so I think that should be the answer.
Could someone point me in the right direction?
Hint: Draw the area of integration and observe that $$\int_{0}^{1} \int_{x}^{1} h(t,x) dt dx = \int_{0}^{1} \int_{0}^{t} h(t,x) dx dt.$$