Example of a Riemann integrable function, which is not bounded

Question

I have to give an example of a function which is Riemann integrable on [0,+∞) but its not bounded. I know about the connection of Riemann Integrability and bounded functions, but this is my assignment and I think there is an intention behind it.

I thought about 1/x. We have done the integral of 1/x and the result is +∞. Would that work?

Edit: I understood that the function 1/x would not work. Would maybe the function f(x)=x work?

Answer 1

$\frac 1 {\sqrt x}$ has finite improper Riemann integral on $[0,1]$.