Determine whether each of the following statements is true or false, and explain why.

Substitution can often be used to turn a complicated integral into a simpler one Substitution can often be used to turn a complicated integral into a simpler one. The definite integral gives an approximation to the area under a curve. The definite integral of a positive function is the limit of the sum of the areas of rectangles. The Fundamental Theorem of Calculus gives a relationship between the definite integral and an antiderivative of a function.

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