# calculation and analysis – Where is the small difference between the result of a normal finite integral and the limitation to definitive integration?

Here is my code.

``````Int1 = Integrate(((1 - Cos(x))/(L^2 (1 - Cos(x)) + 1)^2) Sin(x), {x,
0, Pi})
Int2 = Integrate(((1 - Cos(x))/(L^2 (1 - Cos(x)) + 1)^2) Sin(x), x)
r1 = Int1((1));
r2 = Limit(Int2, x -> Pi) - Limit(Int2, x -> 0);
Plot(r1, {L, -1000, 1000})
Plot(r2, {L, -1000, 1000})
Plot(Abs(r2 - r1), {L, -1000, 1000})
``````

The results of the curves r1, r2 and their difference are, respectively,

I have integration results obtained in two different ways. The results are almost identical since we can see the graph of r1 and r2. The small differences are in order of $$10 ^ {- 25} -10 ^ {- 24}$$ which is acceptable. I want to know where the differences come from. And which one should I use for later calculations?