Hello,

Firstly, you have to prove that , by using the dominated convergence theorem for example (f is continuous over a closed set, --> it is bounded)

Secondly, you have to prove that

In order to show that, write the epsilon definition of this limit : , when (you can "miss" the case x=1, because it's a neglectible case when dealing with integrals... dunno if you know how to deal with it)

Then use the epsilon-delta method on the continuity of f, and you're done.