How Do You Determine the Constant in a Piecewise Probability Density Function?

[someguy54]

if x is a continuous random variable from -1 to 1...how do you find c:

f(x) = c + x , -1 < x < 0
c - x, 0 < x < 1

Do I integrate each one? Where do I go from there? Thanks!

 

[HallsofIvy]

You should know that the integral of a probability density, over the entire interval, is 1: something has to happen so the probability over all possible outcomes has to be 1.
What do you get if you integrate f(x) from -1 to 1 (do as to separate parts and add them- the answer will depend on c). Set that equal to 1 and solve for c.