Reverse Proxy Nginx: depending on path in URL choose proxy_pass

Question

This should be easy to achievable, but I'm totally stuck.

• request: example.com => server1:8080
• request: example.com/everythingelse => server1:8080/everythingelse
• request: example.com/api => server2:8081/api

    server {
        listen 80;
     
        location / {
            proxy_pass         http://server1:8080/;
            proxy_redirect     off;
            proxy_set_header   Host $host;
            proxy_set_header   X-Real-IP $remote_addr;
            proxy_set_header   X-Forwarded-For $proxy_add_x_forwarded_for;
            proxy_set_header   X-Forwarded-Host $server_name;
        }
    
        location /api/ {
            proxy_pass         http://server2:8081/; 
            proxy_redirect     off;
            proxy_set_header   Host $host;
            proxy_set_header   X-Real-IP $remote_addr;
            proxy_set_header   X-Forwarded-For $proxy_add_x_forwarded_for;
            proxy_set_header   X-Forwarded-Host $server_name;
        }
    }