To use PHP's cURL support you must also compile PHP --with-curl[=DIR] where DIR is the location of the directory containing the lib and include directories. In the include directory there should be a folder named curl which should contain the easy.h and curl.h files. There should be a file named libcurl.a located in the lib directory.
Note: Note to Win32 Users
In order to enable this module on a Windows environment, libeay32.dll and ssleay32.dll, or, as of OpenSSL 1.1 libcrypto-*.dll and libssl-*.dll, must be present in your PATH. Also libssh2.dll must be present in your PATH. You don't need libcurl.dll from the cURL site.