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Shamir secret sharing splits into t number of shares with a t-threshold. However, I can find no information online if this scheme provide integrity (or authentication for that matter, which I assume it does not).

Can an adversary forge a share? If not, what hard problem is he faced with. Is it due to the share should be indistinguishable from random (psuedorandom)?

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    $\begingroup$ There are verifiable Shamir schemes in the literature. These do provide integrity. $\endgroup$ – mikeazo May 7 '17 at 20:55
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By Lagrange interpolation...

Does Shamir Secret Sharing provide integrity?

No

Can an adversary forge a share?

Yes

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