This is from the fourth edition Princeton Review book, Chapter 7 review:

#32 - If

, for what value of c is f(x) the probability density function of a random variable X?

I know that the probability density function f(x) has to satisfy

, which for this function is just

,

therefore , but that is not an option. The options are 4/3, 2/3, 0, -2/3, and -4/3. The book claims answer -4/3 is correct, but their explanation also seems way off (they have that the integral above is equal to

, which still doesn't mean c should be -4/3).

Can someone please either verify that I am correct or let me know where I went wrong?