When I integrate
int (-infinity to 5) 1/(x^2+1)dx by using the limit as t --> -infinity of int (t to 5) 1/(x^2+1)dx, I get negative infinity, which means it is DIVERGENT. (antiderivative of 1/(x^2+1) is arctan x, right? and since arctan t as t--> -infinity is -infinity, I get divergent)
But...