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While Set isn't a scoping construct (SC), it is considered one by other SCs outer to it. ref / Set / Details[[-3]] (thanks to Alexey Popkov for correcting me).

Here it is inner to the Module and Module decides not to interfere in this case (don't know why), but you can trick it:

Module[{x},
  Set @@ {f[x_], Integrate[y^2, {y, 0, x}]};
]

?f

f[x$301_]=x$301^3/3

Further reading: Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs

While Set isn't a scoping construct (SC), it is considered one by other SCs outer to it. ref / Set / Details[[-3]] (thanks to Alexey Popkov for correcting me).

Here it is inner to the Module and Module decides not to interfere in this case (don't know why), but you can trick it:

Module[{x},
  Set @@ {f[x_], Integrate[y^2, {y, 0, x}]};
]

?f

f[x$301_]=x$301^3/3

Further reading: Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs

Set it a scoping construct, here inner to the Module and Module decides not to interfere in this case (don't know why), but you can trick it:

Module[{x},
  Set @@ {f[x_], Integrate[y^2, {y, 0, x}]};
]

?f

f[x$301_]=x$301^3/3

Further reading: Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs

While Set isn't a scoping construct (SC), it is considered one by other SCs outer to it. ref / Set / Details[[-3]] (thanks to Alexey Popkov for correcting me).

Here it is inner to the Module and Module decides not to interfere in this case (don't know why), but you can trick it:

Module[{x},
  Set @@ {f[x_], Integrate[y^2, {y, 0, x}]};
]

?f

f[x$301_]=x$301^3/3

Further reading: Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs

Set it a scoping construct, here inner to the Module and Module decides not to interfere in this case (don't know why), but you can trick it:

Module[{x},
  Set @@ {f[x_], Integrate[y^2, {y, 0, x}]};
]

?f

f[x$301_]=x$301^3/3

Set it a scoping construct, here inner to the Module and Module decides not to interfere in this case (don't know why), but you can trick it:

Module[{x},
  Set @@ {f[x_], Integrate[y^2, {y, 0, x}]};
]

?f

f[x$301_]=x$301^3/3

Further reading: Enforcing correct variable bindings and avoiding renamings for conflicting variables in nested scoping constructs