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Integration : Finding Volume of a Disc

Find the volume of y = 1/sqrt(1+x^2) bounded by y=0, x=-1, x=1

I'm using the disc method with a dx function:

V = pi integral( [R(x)]^2 ) dx

Therefore, I have

V = pi integral( [1/sqrt(1+x^2)] ^2 ) dx from -1 to 1

= pi integral( [ 1/(1+x^2) ] ) dx from -1 to 1

I can't figure out how to integrate. Please explain any advanced algebra as my algebra skills are "rusty".

Solution Summary

The volume of a disc is found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.