Considering existing answers, I've copy-pasted and enhanced source code of Integer.parseInt to do the job, and my solution
- does not use potentially slow try-catch (unlike Lang 3 NumberUtils),
- does not use regexps which can't catch too big numbers,
- avoids boxing (unlike Guava's Ints.tryParse()),
- does not require any allocations (unlike int[],Box,OptionalInt),
- accepts any CharSequenceor a part of it instead of a wholeString,
- can use any radix which Integer.parseIntcan, i.e. [2,36],
- does not depend on any libraries.
The only downside is that there's no difference between toIntOfDefault("-1", -1) and toIntOrDefault("oops", -1).
public static int toIntOrDefault(CharSequence s, int def) {
    return toIntOrDefault0(s, 0, s.length(), 10, def);
}
public static int toIntOrDefault(CharSequence s, int def, int radix) {
    radixCheck(radix);
    return toIntOrDefault0(s, 0, s.length(), radix, def);
}
public static int toIntOrDefault(CharSequence s, int start, int endExclusive, int def) {
    boundsCheck(start, endExclusive, s.length());
    return toIntOrDefault0(s, start, endExclusive, 10, def);
}
public static int toIntOrDefault(CharSequence s, int start, int endExclusive, int radix, int def) {
    radixCheck(radix);
    boundsCheck(start, endExclusive, s.length());
    return toIntOrDefault0(s, start, endExclusive, radix, def);
}
private static int toIntOrDefault0(CharSequence s, int start, int endExclusive, int radix, int def) {
    if (start == endExclusive) return def; // empty
    boolean negative = false;
    int limit = -Integer.MAX_VALUE;
    char firstChar = s.charAt(start);
    if (firstChar < '0') { // Possible leading "+" or "-"
        if (firstChar == '-') {
            negative = true;
            limit = Integer.MIN_VALUE;
        } else if (firstChar != '+') {
            return def;
        }
        start++;
        // Cannot have lone "+" or "-"
        if (start == endExclusive) return def;
    }
    int multmin = limit / radix;
    int result = 0;
    while (start < endExclusive) {
        // Accumulating negatively avoids surprises near MAX_VALUE
        int digit = Character.digit(s.charAt(start++), radix);
        if (digit < 0 || result < multmin) return def;
        result *= radix;
        if (result < limit + digit) return def;
        result -= digit;
    }
    return negative ? result : -result;
}
private static void radixCheck(int radix) {
    if (radix < Character.MIN_RADIX || radix > Character.MAX_RADIX)
        throw new NumberFormatException(
                "radix=" + radix + " ∉ [" +  Character.MIN_RADIX + "," + Character.MAX_RADIX + "]");
}
private static void boundsCheck(int start, int endExclusive, int len) {
    if (start < 0 || start > len || start > endExclusive)
        throw new IndexOutOfBoundsException("start=" + start + " ∉ [0, min(" + len + ", " + endExclusive + ")]");
    if (endExclusive > len)
        throw new IndexOutOfBoundsException("endExclusive=" + endExclusive + " > s.length=" + len);
}