a)

and

To do either of these we need

Let's rewrite this a little:

The first integral is elementary, for the second one use the substitution u = -2x and the fact that .

b)

So just plug these into the expression and show that it has a value of 0.

c)

Concavity is determined by the second derivative. So to get the inflection points solve for x. (Hint: for all x, so are there any values of x such that the second derivative is 0?)

To determine the concavity of the function, if the function is concave up, if the function is concave down.

-Dan