diff --git a/opty/tests/test_utils.py b/opty/tests/test_utils.py
index 23a74168..72e36037 100644
--- a/opty/tests/test_utils.py
+++ b/opty/tests/test_utils.py
@@ -200,6 +200,43 @@ def test_invalid_integration_limits(self):
                 sym.Integral(self.x ** 2, (self.t, 0, 1)), self.state_symbols,
                 self.input_symbols, self.unknown_symbols, self.N, 1)
 
+    def test_variable_time(self):
+
+        def expected_obj(free):
+            f = free[2*self.N:-1]
+            return free[-1]*np.sum(f**2)
+
+        def expected_obj_grad(free):
+            f = free[2*self.N:-1]
+            grad = np.zeros_like(free)
+            grad[2*self.N:-1] = 2.0*free[-1]*free[2*self.N:-1]
+            grad[-1] = np.sum(f**2)
+            return grad
+
+        obj_expr = sym.Integral(self.f1**2 + self.f2**2, self.t)
+        obj, obj_grad = utils.create_objective_function(
+            obj_expr, self.state_symbols, self.input_symbols,
+            self.unknown_symbols, self.N, self.h, time_symbols=self.t)
+        np.testing.assert_allclose(obj(self.free), expected_obj(self.free))
+        np.testing.assert_allclose(obj_grad(self.free),
+                                   expected_obj_grad(self.free))
+
+        def expected_obj(free):
+            return free[-1]
+
+        def expected_obj_grad(free):
+            grad = np.zeros_like(free)
+            grad[-1] = 1.0
+            return grad
+
+        obj_expr = sym.Integral(1, self.t)
+        obj, obj_grad = utils.create_objective_function(
+            obj_expr, self.state_symbols, self.input_symbols,
+            self.unknown_symbols, self.N, self.h, time_symbols=self.t)
+        np.testing.assert_allclose(obj(self.free), expected_obj(self.free))
+        np.testing.assert_allclose(obj_grad(self.free),
+                                   expected_obj_grad(self.free))
+
 
 def test_parse_free():