Second fundamental theorem of calculus viewed as a transform?

[vanmaiden]

You see this picture of the second fundamental theorem of calculus

and you are taught in high school / early college calculus that the t is a dummy variable. However, couldn't you view this as some sort of transform? You convert a function f(t) into a function of f(x). Is this a valid way to view this fundamental theorem of calculus?

Thanks,

Vanmaiden

 

[lurflurf]

Yes the theorem is that two transforms are inverse
$$DF=\lim{h\rightarrow 0} \frac{F(x+h)-F(x)}{h}$$
$$If=\int_a^x f(t) dt$$

The fundamental theorem is that
IDF=F
and
DIf=f
which is not obvious