Is it safe to feed 5v dc 1amp to an Arduino uno board?
That's a common newbie question: "What will happen when I use a 1 A power supply for a device which only needs 0.1 A?"
The device will only draw the current it needs. It's the same as on your electricity grid. The nuclear power plant can supply a gigawatt, yet the bulb will only draw the 60 W it needs.
But do you want to apply that 5 V to the power connector? Then the 5 V is too low, you'll need at least something like 6.5 V, otherwise the onboard voltage regulator won't have enough headroom to output 5 V. If you're using the USB connector for a regulated(!) 5 V, then the onboard regulator will be bypassed. Never place an unregulated 5 V on the USB connector, though.
Yes as long as the polarity is correct, the board will only take the current it requires
The 1 Ampère you're mentioning is likely the maximum rating of the power supply, i.e. it cannot sustain higher currents for a long time. However, if you connect your Arduino board (or any other device) to your power supply, the actually flowing current will depend on the voltage U and the resistance R of the device as I = U/R. You can think of this as the Arduino drawing as much power as it needs.
In other words: you must not exceed the maximum voltage, but you don't have to (and cannot in a simple way) adjust the current flowing into the Arduino.