Relay doing opposite to digital pin
The relay module you have is this one from SainSmart:


http://www.sainsmart.com/arduino/arduino-components/relays/sainsmart-2-channel-5v-relay-module-for-arduino-raspberry-pi.html


The schematic is like this:



As you can see you connect VCC to +5V and IN2 to your IO pin.  Setting the IO to LOW will then turn on the LED and the optocoupler together.

But that's not the only way you can connect it up.

Connect VCC to the IO pin and IN2 to GND instead.  Then you set your output HIGH to turn it on.

The arrangement shown in the schematic is commonly done because some MCUs are able to sink more current than they can source thorugh an IO pin.  That is not the case with an Arduino which has symmetric IO pins that can sink and source the same amount of current.