Why is the integral of dt = t + C1

[Dumbledore]

Why is the integral of dt = t + C1

Can someone explain that to me?

Thanks.

 

[lurflurf]

It seem the integral you are interested in is the indefinite type. So you are looking for some function f so that
df=dt
clearly f=t is one such function, but there are others
what if we are intersted in g so that dg=0
but for any c c*dg=c*0=0 also
d(1)=0
but also
d(c)=0

so if du=dv
we can say
d(u-v)=0
but we cannot conclude u=v
since d(u-v)=0
we can conclude
u-v=c for some c

so if df=dt
f=t+c

 

[Dumbledore]

thanks, i understand now.