The sum of all real values of x satisfying the equation (x² - x + 5)x² + 4x = 1 is:

(x² - x + 5)x² + 4x = 1
First possibility is x² + 4x = 0
x = 0, -4
Second possibility is x² - x + 5 = 1
x² - x + 4 = 0
This quadratic equation has no real roots because the discriminant (b² - 4ac) is 1 - 4(4) = -15, which is negative.
Third possibility is x² - x + 5 = -1
x² - x + 6 = 0
This quadratic equation has no real roots because the discriminant (b² - 4ac) is 1 - 4(6) = -23, which is negative.
Therefore, the only real values of x that satisfy the equation are x = 0 and x = -4.
Sum of the integers = 0 + (-4) = -4