Let f be a bounded borel function on the unit hypercube C=$[0,1]^d$ in $\mathbb{R}^d$.Let f be a bounded borel function defined on C.
I need to compute I=$\int_{C}f(x)dx$ by monte carlo integration as follows:Let $X_{1}$,..,$X_{n}$ be independent and uniform on C.Then $f_{n}$=$\dfrac{1}{n}\sum_{j=1}^{n} f(X_{j})$ converges almost surely to I.Let $\epsilon$>0 and find an approximate value of n such that $P(|f_{n}-I|>\epsilon)<0.05$.(We need answer in terms of some integral of f).Also can I find smallest n which works for all functions f such that $sup(|f(x)|:x\in C)\leq1$.