First of all, don't capitalize the first letter of an variables or method names. Following the Java coding conventions, only do that for classes.
What is probably causing your app to crash is you trying to set the text of a label to an integer. The setText method for a TextView needs to take in a string. 
So change:
lblMPG.setText(FuelUsed);
to:
lblMPG.setText(String.valueOf(FuelUsed)); 
Otherwise it might be that it's trying to parse a non-numerical string to an integer.
For exmaple, if the EditText is blank, it will cause your app to crash. To prevent that, try this:
int MilesTravelled = 0, FuelUsed = 0;
try {
    MilesTravelled = Integer.parseInt(txtMilesTravelled.getText().toString());
    FuelUsed = Integer.parseInt(txtFuelUsed.getText().toString());
} catch (NumberFormatException nfe) {
    Toast.makeText(getApplicationContext(), "Error NFE!", 0).show();
    nfe.printStackTrace();
}
This way, it will catch a NumberFormatException error (parsing a string to an integer that can't be represented as an integer, such as "hello"). If it catches the error, it will toast that an error has occurred and your integer variables will remain 0.
Or you could just test if the strings contain only digits using the following regex:
int MilesTravelled = 0, FuelUsed = 0;
if (txtMilesTravelled.getText().toString().matches("[0-9]+")) {
    MilesTravelled = Integer.parseInt(txtMilesTravelled.getText().toString());
} else {
    // contains characters that are not digits
}
if (txtFuelUsed.getText().toString().matches("[0-9]+")) {
    FuelUsed = Integer.parseInt(txtFuelUsed.getText().toString());
} else {
    // contains characters that are not digits
}
If that's not the problem, then make sure you define your variables properly.
txtMilesTravelled and txtFuelUsed should be EditText:
EditText txtMilesTravelled = (EditText)findViewById(R.id.txtMilesTravelled);
EditText txtFuelUsed = (EditText)findViewById(R.id.txtFuelUsed);
And make sure that your R.id.editText actually exists on your layout and that the IDs are the correct ones.
Last thing, make sure FuelUsed is not 0 before calculating MPG because then you are dividing by 0:
int MPG = 0;
if (FuelUsed != 0) {
    MPG = MilesTravelled / FuelUsed; 
}