Question

find the integral of -2/((t^2)+1) [0,1]

Answer 1

integral of -2/((t^2)+1) is -2(arctan(t))
now u can take the limits

Answer 2

thus after taking limits it is
-2(arctan(1)) + 02(arctan(t)) =-2*(pi)/4 =-(pi)/2

[as arctan(1)=(pi)/4 and arctan(0)=0 ]