Question

Evaluate the definite integral using the Fundamental Theorem of Calculus. Give your answer in exact form.

Answer 1

\[\int\limits_{-1}^{1}1/(y^2+1) dy\]

Answer 2

Make the substitution y = tan x

then y^2 + 1 = tan^2 x + 1 = sec^2 x

and dy = sec^2 x dx

It cancels out nicely. Remember to adjust the bounds.