Concept:A definite integral is found by integrating the function first, then using the limits of integration to evaluate the result.Explanation:Integrate each term with respect to x:∫(x2−4x)dx=3x3−24x2=3x3−2x2Therefore,1∫2(x2−4x)dx=[3x3−2x2]12Now substitute the upper limit x=2:323−2(22)=38−8=−316Substitute the lower limit x=1:313−2(12)=31−2=−35Subtract the lower-limit value from the upper-limit value:−316−(−35)=−316+35=−311Answer:−311, which is option D.