FFTC

${\displaystyle \frac{d}{dx}{\int }_a^{x}f(t)dt=f(x)}$

when ${\displaystyle f}$ is continuous on ${\displaystyle [a,b]}$ and ${\displaystyle x}$ in ${\displaystyle (a,b)}$

SFTC

${\displaystyle {\int }_a^{b}f(x)dx=F(b)-F(a)}$

which ${\displaystyle F(x)}$ is the antiderivative of ${\displaystyle f(x)}$, or ${\displaystyle F^{\prime }(x)=f(x)}$

Significance

FFTC shows the connection between derivative and integral, that the differential of the sum of the change becomes the function itself.

SFTC shows the inverse side of FFTC, that the sum of the change of derivative becomes the the change of the function's antiderivative.

Both of the FTC shows the reversibility between derivative and integral.