Add / fix badges for PyPI / versions. (#6158)

Author: tseaver

packages/google-api-core/README.rst

@@ -7,8 +7,8 @@ This library is not meant to stand-alone. Instead it defines
 common helpers used by all Google API clients. For more information, see the
 `documentation`_.
 
-.. |pypi| image:: https://img.shields.io/pypi/v/google-cloud-core.svg
-   :target: https://pypi.org/project/google-cloud-core/
-.. |versions| image:: https://img.shields.io/pypi/pyversions/google-cloud-core.svg
-   :target: https://pypi.org/project/google-cloud-core/
+.. |pypi| image:: https://img.shields.io/pypi/v/google-api_core.svg
+   :target: https://pypi.org/project/google-api_core/
+.. |versions| image:: https://img.shields.io/pypi/pyversions/google-api_core.svg
+   :target: https://pypi.org/project/google-api_core/
 .. _documentation: https://googlecloudplatform.github.io/google-cloud-python/latest/core/