You can't add to an array. You first have to create a bigger array.
int[] newArray = new int[array.length + 1];
Then you have to copy the first half of the array
for(int i = 0; i < midpoint; i++) {
newArray[i] = array[i];
}
Then put the new midpoint in
newArray[midpoint] = 73;
Then copy the other half
for(int i = midpoint + 1; i < array.length; i++) {
newArray[i+1] = array[i];
}
And then newArray has the new midpoint.
Technically the last three steps could be done in any order, but it is much more readable to do them in that order. Now you can call your display method or really do whatever you want with it.
There is a utility method called arrayCopy that can assist with moving the array elements. You may or may not be permitted to use it. It's a bit wordy with its parameters, but is a bit faster than a typical for-loop at runtime because it leverages native code.
int[] newArray = new int[array.length + 1];
System.arrayCopy(array,0,newArray,0,midpoint);
newArray[midpoint] = 73;
System.arrayCopy(array,midpoint,newArray,midpoint+1,array.length - midpoint);
To explain those calls, the arraycopy uses:
System.arrayCopy(arrayFrom,
startPosInArrayFrom,
arrayTo,
startPosInArrayTo,
numElementsToCopy);