Find the integral of f(x)= x^3 + 2x^2 + 1
Let's work our way from left to right. Starting with the x3 term we will take the integral with respect to x. First we add one to the power we get x4, next we take the coefficient and divide it by the new exponent leaving us with 1/4. Therefore our first term is (1/4)x4 . Moving on we take 2x2 and add one to the power making x3. Take the coefficient and divide it by the new exponent getting 2/3. Our second term is then (2/3)x3. With the last term we have an exponent of 0 because x0=1. Add one to the exponent to get x1 and divide the coefficient by the new exponent. The last term becomes x. The integral of f(x) is (1/4)x2 + (2/3)x3 + x + C. Since this is an indefinite integral (meaning we have no limits) we leave C to be any constant.
You can check your answer by taking the derivative of what you have to confirm it is the same as what the question gave for f(x).
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