Calculate , where is the standard normal random variable (with density function ).

So am I to calculate ?

If I'm approaching this correctly, that leaves me with a mess stickier than a barrel of molasses which I don't know how to handle at all. I mean, I know that the integral of f(x) is F(x) where F(x) is the cumulative distribution function for the standard normal distribution, but I don't know what that is explicitly nor how to calculate it, let alone what is being asked here. In lecture, we have used tables of values for , where (I assume) is this F(x), to approximate definite integrals of f(x) but I do not see how that might help here...so lost.

Suggestions, please?