∫[-2,2] f(t)dt
=∫[-2,0](1/π)*(1/(1+t^2))dt +∫[0,2]e^-2tdt
=(1/π)arctan(2)+(-1/2)[e^(-4)-1]
∫(-∝,+∝)f(t)dt
=∫(-∝,0] (1/π)*(1/(1+t^2))dt +∫[0,+∝)e^(-2t)dt
=(1/π)*(π/2)+)+(-1/2)[0-1]
=1/2+1/2=1
∫[-2,2] f(t)dt
=∫[-2,0](1/π)*(1/(1+t^2))dt +∫[0,2]e^-2tdt
=(1/π)arctan(2)+(-1/2)[e^(-4)-1]
∫(-∝,+∝)f(t)dt
=∫(-∝,0] (1/π)*(1/(1+t^2))dt +∫[0,+∝)e^(-2t)dt
=(1/π)*(π/2)+)+(-1/2)[0-1]
=1/2+1/2=1