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So im trying to understand exactly what the indefinte integral means?

heres my train of thought...

if our function F(x) = x

^{2}then its derivative is F'(x) = 2x

and this F'(x) will give you the slope of a tangent line to F(x) at any point x .

If the graph was Distance vs. time this slope would be the velocity in lets say m/s.

Now with the integral.. lets say F(x) now represents velocity vs time...

then i understand if i take the DEFINITE integral on an interval of this graph i will get the area under the curve of F(x)= x^2... and lets say again its m/s vs time (s) then (m/s)(s) = m i.e. velocity x time = displacement.....

so what exactly is happening if i take the indefinite integral? i'm having trouble visiualising this... does is it trying to find the area under the entire function? i,e to infinity.. this doesnt make sense.. can someone please explain that too me?