The sign issue is already fixed on master. I bisected the fix to 352587a from gh-26173.

There are other problems though. The definite integral should not have x. The reason is because of a bug to do with replacing symbols with assumptions:

In [16]: i1 = integrate(sin(a*(x+pi))**2, (x, -pi, -pi/2))

In [17]: i2 = + pi/4 - sin(pi*x)/(4*x)

In [18]: i1
Out[18]: 
π   sin(π⋅x)
─ - ────────
4     4⋅x   

In [19]: i2
Out[19]: 
π   sin(π⋅x)
─ - ────────
4     4⋅x   

In [20]: i1 == i2
Out[20]: False

In [21]: srepr(i1)
Out[21]: "Add(Mul(Rational(1, 4), pi), Mul(Integer(-1), Rational(1, 4), Pow(Symbol('x', real=True, positive=True), Integer(-1)), sin(Mul(pi, Symbol('x', real=True, positive=True)))))"

In [22]: srepr(i2)
Out[22]: "Add(Mul(Rational(1, 4), pi), Mul(Integer(-1), Rational(1, 4), Pow(Symbol('x', real=True), Integer(-1)), sin(Mul(pi, Symbol('x', real=True)))))"

The result returned from integrate has Symbol('x', real=True, positive=True) rather than Symbol('x', real=True). Somewhere the symbol got replaced with one that has the positive assumption but then was not replaced back. Presumably this is what results in it still having x because substituting limits for the wrong symbol (with different assumptions) failed.

the x in the result is my error ... x and a have the same symbol in the definition. It of course should be

a = symbols('a', real=True, positive=True)
and then I get the result
-pi/4 + sin(pi*a)/(4*a)

Oh, of course. In that case this is fixed on master by the commit I referred above:

In [1]: from sympy import *
   ...: x = symbols('x', real=True)
   ...: a = symbols('a', real=True, positive=True)
   ...: integrate(sin(a*(x+pi))**2, (x, -pi, -pi/2))
Out[1]: 
π   sin(π⋅a)
─ - ────────
4     4⋅a   

This issue can be closed if a test is added for this case.

@oscarbenjamin sir this test is okay in test_integrals.py
def test_definite_integral_sign_issue_fixed or test_issue_26566():
x = symbols('x', real=True)
a = symbols('a', real=True, positive=True)
assert sin(a*(x+pi))**2 == simplify(pi/4 - sin(pi * a)/(4 * a)) can i make a PR for this or some problem in that

The test looks fine to me