Please give me some guidlance on the following problem :

LetX be a random variable such that its values lie in the interval [−1 1] and consider the function

f: [−1 1]- R f (x) = ((x\2) +1 ) * e^(x-1) .

a) Prove that f can be the probability density of X.

b) Compute the expected value of X.

Many thanks,