Arduino Uno analog pins seem to be connected

I'm new to the Arduino (I have Arduino Uno) and recently was playing around with analogWrite. I set up two potentiometers and two LEDs (both LEDs attached to PWM pins). However, when I have only one potentiometer attached it controls both LEDs. I do not understand why this is happening since the LEDs rely on different potentiometers that are attached to different analog pins. Why is this happening?

#define LED1 5
#define LED2 6
#define POT1 A0
#define POT2 A1

int val1, val2;
void setup() {
  pinMode(LED1, OUTPUT);
  pinMode(LED2, OUTPUT);
}

void loop() {
  val1 = analogRead(POT1);
  val2 = analogRead(POT2);
  analogWrite(LED1, val1);
  analogWrite(LED2, val2);
}

These 2 reads will happen very quickly

val1 = analogRead(POT1);
val2 = analogRead(POT2);

Others have reported better results by doing 2 reads and ignoring the results of the first one, gives the analog multiplexer a chance to catch up with the changing data.
If you did a serial write of the data after the 2nd analogwrite, you would doubtless find the data to be very similar.

Thanks I appreciate the response!

Do you have it working now?