When states gave up some of their power to the federal government, they generally received protection from the federal government in return. The federal government was established to provide a framework for national defense, manage interstate relations, and uphold certain rights and freedoms, ensuring states are protected against both external threats and internal conflicts.
The other options provided, such as negotiating with foreign countries or determining federal responsibilities, are not correct as states are limited in those powers under the U.S. Constitution. The integration of public schools is also primarily a result of federal intervention rather than a guarantee in exchange for state power.