An integral is defined as the area under the curve of a function. A summation is defined as the sum of outputs given a specific set of inputs into a function. An example is as follows: given f(x) = x^2 from 0 to 5 the integral can be calculated as (x^3)/3 from 0 to 5 which equals 125/3. (Assuming you know how to calculate an integral). If the same function was placed beside of a summation notation with the same interval (from 0 to 5) we would add the outputs: summation = f(1) + f(2) + f(3) + f(4) + f(5). Using this we can then plug in our numbers of the given interval to give us 1 + 4 + 9 + 16 + 25. The final summation would equal 55 in this example.