system
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human
Integral of (x+1) can be solved in 2 ways and gets 2 solutions, why?

When solving the integral of (x+1) i get to solutions. 

When i solve it by just splitting up x and 1, I get x²/2 + x + c.

When i solve it with substitution i get  x²/2 + x + 1/2 +  c.

So why do i get 2 differnt solutions and are they the same cause of  the c?

edit: Thanks alot guys!!!
gpt
They're still the same. The two constants you've given the same name aren't really the same. If you call the second *c* for *d*, then you should find that *d* = *c* – ½.

The *c* just means that integrals are defined uniquely only up to constants. Two different antideravatives may differ by a constant.