I know that according to the first fundamental theorem of calculus:(adsbygoogle = window.adsbygoogle || []).push({});

$$\frac{d}{dx} \int_a^x f(t) dt = f(x)$$

I also know that if ##F## is an antiderivative of ##f##, then the most general antiderivative is obtained by adding a constant.

My question is, can every single antiderivative of ##f## be expressed as:

$$\int_{a_n}^x f(t) dt = F_n (x)$$

where ##a_n## is some constant (every ##a_n## generates a different antiderivative)? Or is it not possible in some cases?

In other words, caneveryantiderivative of a function be expressed as a definite integral (one term only)?

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# Antiderivatives and the fundamental theorem

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