Using external power source

Wilfa:
Arduino is powered by 5.0v so you need a converter (L7805) or you can use 3 1.5v batteries (3*1.5 = 4.5)

I have concerns about this information.
The official website says that you can power up 6v-20v, but is recommended 7v-12v. Powering with VIN pin.
We just need to connect the 9v battery. Like this:

Am i right?
Oficial site http://arduino.cc/en/Main/ArduinoBoardUno:

"The board can be supplied with power either from the DC power jack (7 - 12V), the USB connector (5V), or the VIN pin of the board (7-12V). Supplying voltage via the 5V or 3.3V pins bypasses the regulator, and can damage your board. We don't advise it."

"If supplied with less than 7V, however, the 5V pin may supply less than five volts and the board may be unstable. If using more than 12V, the voltage regulator may overheat and damage the board. The recommended range is 7 to 12 volts."