As I understand, any software working with X.509 certificates may have own basis to decide, whether a certificate is trusted or not. 

AFAIK OpenSSL just consults a list (such as, for example, /etc/ssl/certs) and checks if the certificate is present there.

Is there a way for OpenSSL to list all certificates which it trusts? I know that I can consult that file myself (on my particular installation of OpenSSL), but is there a (installation-independent) way to get the trusted list from OpenSSL itself?