Suppose f has absolte minimum value m and absolute maximum value M. Between what two values must integral 2 to 4 f(x)dx lie?
mmm
If M and m are both positive then the integral will be between (4-2)*m (smallest) and (4-2)*M (largest)
If M or n can be negative and you do not know which one has the biggest absolute value then it gets more complicated.
Remember that an integral is the sum of infinitely tiny cross-section areas.