What is your difficulty? Do you know the definition of "uniformly continuous"?
(First point you need to deal with is that you cannot prove the statement as given- it isn't true! f(x)= sin(x)/x is not defined at x= 0 and so cannot be continuous there. The function "f(x)= sin(x)/x for x not equal to 0, f(0)= 1" is uniformly continuous in R.)