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## Homework Statement

I hope this is in the right forum, because this is a question on theory and not related to a specific problem.

I was reading onlne about the Fundamental Theorem of Calculus. On one site the author wrote:

[tex]F(x) = \int_{0}^{x} f(t) dt[/tex]

Later, he wrote:

[tex]\int_{a}^{b} f(x) dx = \int_{0}^{b} f(x) dx - \int_{0}^{a} f(x) dx = F(b) - F(a)[/tex]

However, I've been taught that

[tex]\int_{a}^{b} f(x) dx[/tex]

equals the indefinite integral of f(x) evaluated at b minus the indefinite integral of f(x) evaluated at a.

This leads me to ask:

Is the indefinite integral of a function, lets call it [itex]G(x)[/itex], the same as the definite integral [tex]\int_{0}^{x} f(t) dt[/tex] ?

I know this is a really basic question.

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Edited to fix what Mark44 pointed out

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