How to find upper and lower bound of a definite integral given an unknown equation?

Finding the upper and lower bounds for a definite integral without an equation is pretty hard because how can we find the upper and lower bounds of  definite integral if there is no equation given. But I will teach you how to find the lower and upper bounds of a definite integral, when the equation is like this 

 

So, i integrate this, 


I know I have a minimum at x=3 because;
f(t )= t^2 − 6t + 11
f′(t) = 2
t−6 = 0
2(t−3) = 0
t = 3
f(5) = 4
f(1) = −4