IMathAS-libretexts

Suppose $\displaystyle {f}'{\left({x}\right)}={g{{\left({x}\right)}}}$ and $\displaystyle {g}'{\left({x}\right)}={h}{\left({x}\right)}$ . What does the fundamental theorem of calculus say? Choose the correct response.

$\displaystyle {\int_{{3}}^{{5}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}={g{{\left({5}\right)}}}-{g{{\left({3}\right)}}}$
$\displaystyle {\int_{{3}}^{{5}}}{g{{\left({x}\right)}}}{\left.{d}{x}\right.}={h}{\left({5}\right)}-{h}{\left({3}\right)}$
$\displaystyle {\int_{{3}}^{{5}}}{g{{\left({x}\right)}}}{\left.{d}{x}\right.}={f{{\left({5}\right)}}}-{f{{\left({3}\right)}}}$
$\displaystyle {\int_{{3}}^{{5}}}{f{{\left({x}\right)}}}{\left.{d}{x}\right.}={h}{\left({5}\right)}-{h}{\left({3}\right)}$
$\displaystyle {\int_{{3}}^{{5}}}{h}{\left({x}\right)}{\left.{d}{x}\right.}={f{{\left({5}\right)}}}-{f{{\left({3}\right)}}}$

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