# Is it mathematically correct to write the primitive of a function in this way : $F(x)=\int f(x)dx$

Is it mathematically correct to write the primitive of a function in this way : $$F(x)=\int f(x)dx$$

or should we absolutely change the variable name : as in $$F(t)=\int f(x)dx$$ ? (that is : not use the same variable inside the integral)

• The first one is better form. Even better: $F(x) = \int f(x)dx + C$. For example, $$\cos x = \int \sin x \space dx + C.$$ The second one is more appropriate for definite integrals, for example $$F(t) = \int_a^t f(x)dx.$$
– D_S
Mar 6, 2021 at 16:51

$$F(x)=\int f(x)dx$$ is very common. So you will never convince everyone not to do it.
However $$F(t)=\int f(x)dx$$ is worse. The RHS does not reveal what the variable is.
Some peculiar people may write $$F = \int f$$, which is OK as far as variables are concerned.
Related: Do not write $$F(x)=\int_0^x f(x)dx$$. That has $$x$$ used for two different things in the same formula.
But it is OK to write $$F(t)=\int_0^t f(x)dx$$. This time the RHS does reveal what the variable is.