I have to use the integral test to figure out if the summation of 1/(n^{2}+4) converges or diverges.

the first thing I did was set it to a function (1/(x^{2}+4)) then I set up an integral from 1 to infinity for that function. Then took the limit as b>infinity from 1 to b for f(x).

I'm stuck here. The solution manual says that I should get the following:

lim as b>inf [(1/2)Tan^{-1}(x/2)] from b to 1.

Can someone explain this to me please? I can figure out the steps after but I don't understand this step.