Apply suggestions from code review

sympy/simplify/simplify.py

@@ -515,6 +515,10 @@ def simplify(expr, ratio=1.7, measure=count_ops, rational=False, inverse=False):
     kwargs = dict(ratio=ratio, measure=measure,
         rational=rational, inverse=inverse)
 
+    # no routine for Expr needs to check for is_zero
+    if isinstance(expr, Expr) and expr.is_zero and expr*0 is S.Zero:
+        return S.Zero
+
     _eval_simplify = getattr(expr, '_eval_simplify', None)
     if _eval_simplify is not None:
         return _eval_simplify(ratio=ratio, measure=measure, rational=rational, inverse=inverse)

sympy/simplify/tests/test_simplify.py

@@ -806,3 +806,9 @@ def test_issue_15965():
     assert simplify(A + B) == anew + bnew
     assert simplify(A) == anew
     assert simplify(B) == bnew
+
+
+def test_issue_7971():
+    z = Integral(x, (x, 1, 1))
+    assert z != 0
+    assert simplify(z) is S.Zero