MATL, 6 bytes

QJi-h)

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Input is given as 1) number of elements to trim from the start; 2) number of elements to trim from the end; 3) array. Explanation

Q   % Implicit input (1). Increment by 1, since MATL indexing is 1-based.
Ji- % Complex 1i minus real input (2). In MATL, the end of the array is given by `1i`.
h   % Concatenate indices to get range-based indexing 1+(1):end-(2).
)   % Index into (implicitly taken) input array. Implicit display.