For what value of c is f a pdf?

[njmiano]

I am doing some practice problems, and cannot figure this one out.
Let f(x) = c/(1+x^2)
For what value of c is f a pdf?
I understand that in order for it to be a probability density function, it's integral from a to b must equal one, and I know that the answer is 1/pi, but I have no idea how to solve for c.
Thanks in advance for any help.

 

[Deleted member 4993]

I am doing some practice problems, and cannot figure this one out.
Let f(x) = c/(1+x^2)
For what value of c is f a pdf?
I understand that in order for it to be a probability density function, it's integral from a to b must equal one, and I know that the answer is 1/pi, but I have no idea how to solve for c.
Thanks in advance for any help.

Hint:

\(\displaystyle \int \frac{1}{1+x^2} dx \, = \, \tan^{-1}(x) \, + \, C\)

 

[njmiano]

Thanks,
I got it now. I had been equating arc lengths and areas for the last 6 hours, and must have forgotten the easier stuff.