INTEGRAL AND INEQUALITY

see the function f(x) = x² - x..
f(x) is increasing for x > 1/2 and decreasing for x < 1/2..
so in the interval (0,2) ..f(x) will be maximum at x = 2 and minimum at x = 1/2..
put the value x = 1/2 and x = 2 in f(x) and u will get

e^-1/4 < e^f(x) < e²

now integrate with respect to x and put the limits..u will get the required equation

thnks govind and SR