You'd have to bias your analog inputs to 1/2 of your supply voltage, in this case 2.5Volts (5V / 2)
You can use a voltage divider here, 2 equal value resistors.
So your 2.5Volts is now your "0 V" line. That gives you + 2.5VDC and -2.5VDC range.
A measured 3.5volts is your +1V input.
A measured 1.5volts is your -1V input.