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From the wallet address, the address string looks like :-
43qKZHxtoDJGteTbsSM9Eo31bFxCsE8WzMbpCvFVzWuEjfCMV5TmmVsZhvS472NgV8DQ1XMNimBbgavj3nX9XD7178Pbt6C
I have created an integrated address, which I am told consists of the above address and payment id but still refers to the same wallet.
Is it possible to discover my wallet address from the integrated address ?
Yes, you can use Box 8 in the Check Address section of this tool: https://xmr.llcoins.net/addresstests.html
Yes, the purpose of those is not to conceal the address but to pack the payment ID together with it.
The address is never actually recorded to the blockchain and no payment can be linked to an address by 3rd parties so re-use is not a problem. This is also the reason we need payment IDs, which are just a message attached to a TX. We need this because the recipient is usually using the same wallet for many transfers but he can't even tell from where some funds come so you need to add a little random message so you can tell him: look, TX with the message "xyz" is from me.
Integrated addresses are indeed trivially split into their standard address and payment ID components: use the integrated_address command in monero-wallet-cli:
integrated_address INTEGRATEDADDRESSHERE
Via RPC, you can also use the split_integrated_address call:
curl -X POST http://127.0.0.1:8888/json_rpc -d '{"jsonrpc":"2.0","id":"0","method":"split_integrated_address","params":{"integrated_address":"INTEGRATEDADDRESSHERE"}}' -H 'Content-Type: application/json'
